[seqfan] Sequence that contains A028242
jnthn stdhr
jstdhr at gmail.com
Wed Oct 4 20:49:43 CEST 2017
Hello seqfans.
The sequence 0,1,1,0,1,2,1,1,1,3,... is not in the database. It is
produced by the following:
a(0) = 0, a(1) = 1, a(2) = 1, a(3) = 0; a(n) = { if n is even, a(n - 2);
if n is odd, a(n - 3) + a(n - 4) }
The odd terms appear to produce A028242 (Follow n+1 by n. Also
(essentially) Molien series of 2-dimensional quaternion group Q_8).
With the lookup of "0 1 1 0 1 2 1 1 1 3 1 2 1 4 1 3 1 5"
superseeker suggests the following generating functions:
(1)
"Generating function(s) and type(s) are:
2 3 4 5 6 [[RootOf(y - _Z + (-y - 1) _Z + _Z - y _Z - _Z + (y + 1) _Z )],
revogf]
revogf = reversion of ordinary generating function"
(2)
"TRY "GUESSS", HARM DERKSEN'S PROGRAM FOR GUESSING A GENERATING FUNCTION
FOR A SEQUENCE.
Guesss suggests that the generating function F(x) may satisfy the following
algebraic or differential equation:
x^6-x^5+x^3-x^2-x+(x^6-x^2-x^4+1)*F(x) = 0
If this is correct the next 6 numbers in the sequence are:
[1, 4, 1, 6, 1, 5] "
The next six terms in (2) are correct. I don't understand (1).
Since it appears this is just A028242 with ones inserted between terms,
should I bother to submit this sequence?
-Jonathan
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