# [seqfan] Re: (no subject)

Hagen von Eitzen hagen at von-eitzen.de
Sun Jun 21 23:51:10 CEST 2009

```lajos66 at t-online.hu schrieb:
> Joerg!
>
> This is comment, new.
> Analog: Rencontres numbers, derangements numbers
> definitions.....
>
> All:
> A000079 Powers of 2 vvv, vvz, vzv, vzz, zvv, zvz, zzv, zero
> (0) or free u's.               (uuu) >>three u'-s
> A000244 Powers of 3
> A000302 Powers of 4
> A000351 Powers of 5
> A000400 Powers of 6
> A000420 Powers of 7
> A001018 Powers of 8
> A001019 Powers of 9
> A011557Powers of 10
> etc...
> all:..........containing exactly zero (0) or free
> u's..............
>
> bad or wrong:  zero (0) and free u's. this is .
> good : zero or (0) or free u's, or without or nullity or
> null or nil u's, etc...
>
> This is simple:six (6) u's
>
> A002409                      2^n*C(n+6,6). Number of 6D
> hypercubes in an (n+6)-dimensional hypercube.>>>>With a
> different offset, number of n-permutations (n>=6) of 3
> objects: u, v, z with repetition allowed, containing exactly
> six (6) u's.
>
> Analogia:fixed point free= 0, zero fixed point. ( fixed
> point free element (derangement))
>
> Sorry, i dont speak english.
>
> All searchingOEIS: "With a different offset, number of
> n-permutations"
> Displaying 1-10 of 83 results found.
>
> a(3)=8 because we have vvv, vvz, vzv, vzz, zvv, zvz, zzv,
> zzz >> without u'-s.
>
> a(4)=16 because we have
> vvvv  vvvz  vvzv  vzvv  zvvv  vvzz  vzvz  zvvz  vzzv  zzvv
> zvzv  zzzv  zzvv   zvzz vzzz zzzz (16 without (0), zero, ...
> u'-s.)
>
>
So the u is really redundant (the sequences have zero us, as well as 0
t's, 0 q's, etc.
And we are left with the strings of n letters from the alphabet  {v,z} -
or more eveidently {0,1}, i.e.
000, 001, 010, 011, 100, 101, 110, 111
etc.

> etc...
>
> sincerely
> Zerinvary Lajos
> Hungary
>
> --- On Sun, 6/21/09, Joerg Arndt <arndt at jjj.de> wrote:
>
>
>     From: Joerg Arndt <arndt at jjj.de>
>     Subject: Q regarding comment in A000079 (Powers of 2)
>     To: seqfan at list.seqfan.eu
>     Cc: zerinvarylajos at yahoo.com
>     Date: Sunday, June 21, 2009, 5:10 AM
>
>     This comment needs corrections and clarifications:
>
>     With a different offset, number of n-permutations (n>=0)
> of 3 objects:
>     u, v, z with repetition allowed, containing exactly zero
> (0) or free
>     u's. For example, a(3)=8 because we have vvv, vvz, vzv,
> vzz, zvv, zvz,
>     zzv, zzz.
>     - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2008
>
>     Firstly, "With a different offset" seems wrong,
>     a(3)==8 in the example and indeed a(3)==8 in the seq.
>
>     Also: "containing exactly zero (0) or free"
>     free --> three?
>
>     Examples for n==4 or n==5 may be instructive.
>     From what I see the comment seems to be just wrong.
>
>
>
>
>
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>
>
>

```