[seqfan] Re: 2,0,2,8,210;0,2,0,10,208

Tue Mar 23 10:36:40 CET 2021

Well, if those sequences are correct, they should definitely be added to
the OEIS!

The reason I am a little hesitant is that we have a large number of similar
sequences already.

Take a look at A001528, which is

%I M1991 N0785

%S 1,1,2,10,208,615904,200253951911058

%N NPN-equivalence classes of switching functions of exactly n variables.

(with many more lines)  and    A000610, A000616, etc

and also the  entry in the Index to the OEIS for Boolean functions:

*Boolean functions, sequences related to :*
Boolean functions, balanced: A000721 <http://oeis.org/A000721>Boolean
functions, cascade-realizable: A005608 <http://oeis.org/A005608>, A005609
<http://oeis.org/A005609>, A005610 <http://oeis.org/A005610>, A005611
<http://oeis.org/A005611>, A005613 <http://oeis.org/A005613>, A005619
<http://oeis.org/A005619>, A005749 <http://oeis.org/A005749>Boolean
functions, Dedekind's problem: see Boolean functions, monotone (Dedekind's
problem)Boolean functions, fanout-free: A005737 <http://oeis.org/A005737>,
A005736 <http://oeis.org/A005736>, A005742 <http://oeis.org/A005742>,
A005738 <http://oeis.org/A005738>, A005740 <http://oeis.org/A005740>,
A005612 <http://oeis.org/A005612>, A005615 <http://oeis.org/A005615>,
A005617 <http://oeis.org/A005617>, A005743 <http://oeis.org/A005743>,
A005741 <http://oeis.org/A005741>Boolean functions, inequivalent, under
action of various groups (1): A000133 <http://oeis.org/A000133>, A000214
<http://oeis.org/A000214>, A000231 <http://oeis.org/A000231>, A000585
<http://oeis.org/A000585>, A000614 <http://oeis.org/A000614>, A001289
<http://oeis.org/A001289>, A003180 <http://oeis.org/A003180>, A008842
<http://oeis.org/A008842>, A011782 <http://oeis.org/A011782>, A028401
<http://oeis.org/A028401>, A028402 <http://oeis.org/A028402>, A028403
<http://oeis.org/A028403>Boolean functions, inequivalent, under action of
various groups (2): A028404 <http://oeis.org/A028404>, A028405
<http://oeis.org/A028405>, A028406 <http://oeis.org/A028406>, A028407
<http://oeis.org/A028407>, A028409 <http://oeis.org/A028409>, A028410
<http://oeis.org/A028410>, A028411 <http://oeis.org/A028411>, A049461
<http://oeis.org/A049461>, A051460 <http://oeis.org/A051460>, A051502
<http://oeis.org/A051502>, A053040 <http://oeis.org/A053040>, A057132
<http://oeis.org/A057132>Boolean functions, invertible: A001038
<http://oeis.org/A001038>, A000656 <http://oeis.org/A000656>, A000653
<http://oeis.org/A000653>, A000722 <http://oeis.org/A000722>, A000654
<http://oeis.org/A000654>, A000725 <http://oeis.org/A000725>, A000724
<http://oeis.org/A000724>, A000723 <http://oeis.org/A000723>, A001537
<http://oeis.org/A001537>, A000652 <http://oeis.org/A000652>, A128904
<http://oeis.org/A128904>Boolean functions, irreducible: A000616
<http://oeis.org/A000616>*Boolean functions, Knuth's tables. D. E. Knuth,
The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79, has three
useful lists of Boolean functions, which are as follows. Table 3: A001146
<http://oeis.org/A001146>, A001146 <http://oeis.org/A001146>, A000372
<http://oeis.org/A000372>, A001206 <http://oeis.org/A001206>, A102897
<http://oeis.org/A102897>, A109457 <http://oeis.org/A109457>, A000609
<http://oeis.org/A000609>, A000079 <http://oeis.org/A000079>, A102449
<http://oeis.org/A102449>. Table 4: A003180 <http://oeis.org/A003180>,
A057132 <http://oeis.org/A057132>, A003182 <http://oeis.org/A003182>,
A008840 <http://oeis.org/A008840>, A193675 <http://oeis.org/A193675>,
A109458 <http://oeis.org/A109458>, A109455 <http://oeis.org/A109455>,
A109460 <http://oeis.org/A109460>. Table 5: A000370
<http://oeis.org/A000370>, A001531 <http://oeis.org/A001531>, A001529
<http://oeis.org/A001529>, A001532 <http://oeis.org/A001532>, A000616
<http://oeis.org/A000616>.Boolean functions, minimal numbers of elements
needed to realize any: A056287 <http://oeis.org/A056287>*, A057241
<http://oeis.org/A057241>*, A058759 <http://oeis.org/A058759>*Boolean
functions, monotone (Dedekind's problem): A000372 <http://oeis.org/A000372>
*, A003182 <http://oeis.org/A003182>*, A007153 <http://oeis.org/A007153>*,
A001206 <http://oeis.org/A001206>*, A014466 <http://oeis.org/A014466>*Boolean
functions, monotone (Dedekind's problem): see also Dedekind's problem
<https://oeis.org/wiki/Index_to_OEIS:_Section_De#Dedekind>Boolean
functions, monotone (Dedekind's problem): see also A016269
<http://oeis.org/A016269>, A047707 <http://oeis.org/A047707>, A051112
<http://oeis.org/A051112>, A051113 <http://oeis.org/A051113>, A051114
<http://oeis.org/A051114>, A051115 <http://oeis.org/A051115>, A051116
<http://oeis.org/A051116>, A051117 <http://oeis.org/A051117>, A051118
<http://oeis.org/A051118>Boolean functions, nondegenerate: A000371
<http://oeis.org/A000371>*, A000618 <http://oeis.org/A000618>, A003181
<http://oeis.org/A003181>, A001528 <http://oeis.org/A001528>Boolean
functions, see also (1): A000157 <http://oeis.org/A000157>, A000370
<http://oeis.org/A000370>, A000612 <http://oeis.org/A000612>, A000613
<http://oeis.org/A000613>, A001087 <http://oeis.org/A001087>, A005530
<http://oeis.org/A005530>, A005581 <http://oeis.org/A005581>, A005744
<http://oeis.org/A005744>, A005756 <http://oeis.org/A005756>, A018926
<http://oeis.org/A018926>, A036240 <http://oeis.org/A036240>, A037267
<http://oeis.org/A037267>Boolean functions, see also (2): A037843
<http://oeis.org/A037843>, A051185 <http://oeis.org/A051185>, A051355
<http://oeis.org/A051355>, A051360 <http://oeis.org/A051360>, A051361
<http://oeis.org/A051361>, A051368 <http://oeis.org/A051368>, A051375
<http://oeis.org/A051375>, A051376 <http://oeis.org/A051376>, A051381
<http://oeis.org/A051381>, A056778 <http://oeis.org/A056778>Boolean
functions, see also canalizing functions
<https://oeis.org/wiki/Index_to_OEIS:_Section_Ca#canalizing>Boolean
functions, see also switching networks
<https://oeis.org/wiki/Index_to_OEIS:_Section_Sw#switching>Boolean
functions, see also threshold functions
<https://oeis.org/wiki/Index_to_OEIS:_Section_Th#threshold>Boolean
functions, self-complementary: A000610 <http://oeis.org/A000610>*, A001320
<http://oeis.org/A001320>*, A053037 <http://oeis.org/A053037>Boolean
functions, self-dual monotone: A001206 <http://oeis.org/A001206>*Boolean
functions, self-dual: A001531 <http://oeis.org/A001531>*, A006688
<http://oeis.org/A006688>*, A002080 <http://oeis.org/A002080>, A008840
<http://oeis.org/A008840>, A008841 <http://oeis.org/A008841>Boolean
functions, triangle of numbers of: A039754 <http://oeis.org/A039754>,
A051486 <http://oeis.org/A051486>*, A053874 <http://oeis.org/A053874>*,
A052265 <http://oeis.org/A052265>*, A054724 <http://oeis.org/A054724>*,
A022619 <http://oeis.org/A022619>*, A059090 <http://oeis.org/A059090>Boolean
functions, unate: A003183 <http://oeis.org/A003183>

Does the manuscript that you mention explain how your sequences are related
to existing OEIS entries?

How did you calculate these numbers?  They are notoriously difficult to do
by hand!

If you used a computer, can you get a couple more terms?

Best regards
Neil

Neil J. A. Sloane, President, OEIS Foundation.
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

On Tue, Mar 23, 2021 at 3:45 AM Nollaig MacKenzie via SeqFan <
seqfan at list.seqfan.eu> wrote:

>
> I wonder whether these sequences are worth
> submitting to OEIS:
>
> SR(N): 2,0,2, 8,210...
> SD(N): 0,2,0,10,208...
>
> (N=0,1,2,3,4...)
>
> SR(N) is the number of N variable nondegenerate
> self-reflecting truth-tables, SD(N) the number
> of nondegenerate N variable self-dual tables.
>
> Table t1 is a reflection of table t0 if the
> last column of t1 is that of t0 reversed, as
> the table for 'p nand q' would be for that of
> 'p or q'.
>
> Table t1 is a dual of t0 if the last column of t1
> is the last of t0 reversed and negated
> ('p and q'; 'p or q').
>
> An example of a self-reflection would be the table
> for 'p xor q': 0 1 1 0.
>
> A self-dual, 'p': 0 1.
>
> Formulae for calculating SR and SD:
>
> SR(0) = 2; for N>0, SR(N) = T(N-1) - SR(N-1)
> SD(0) = 0; for N>0, SD(N) = T(N-1) - SD(N-1)
>
> Where T(N) is given by A000371 in OEIS (The
> number of N variable nondegenerate truth-tables
> 2,2,10,218,64594...)
>
> The sequences SR and SD must have been noticed,
> but I don't find them in OEIS. I don't know whether to
> submit them: (a) I don't know whether they are significant
> enough; (b) I don't have a way of calculating SR(N)
> directly from N.
>
> I have a short paper with a little more detail on this
> that I'm happy to send to anyone interested.
>
> Best wishes,
> Nollaig MacKenzie
> gnaillo at hushmail.com
>
> Sent using Hushmail
>
>
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>