A088456 Number of integer sequences [y(1),...,y(n)] such that |y(i)-y(i+1)|<=1, 1=y(1)<=y(i)<=y(n).

1, 1, 2, 4, 9, 22, 56, 146, 387, 1039, 2819, 7717, 21287, 59105, 165038, 463089, 1304945, 3690970, 10474213, 29811119, 85070660, 243340754, 697571153, 2003636629, 5765473829, 16617825248, 47971281916, 138677926537, 401428641619, 1163442587941, 3375837976468, 9805869144592, 28512102516914

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Danai Deligeorgaki and Krishna Menon, How to bounce your canon permutation, arXiv:2603.22565 [math.CO], 2026. See p. 29.

Example

[1,1,1],[1,1,2],[1,2,2],[1,2,3] are the a(3)=4 sequences.

Prog

(PARI) a(n)=local(p0, p1, p2); if(n<0, 0, p1=1; polcoeff(sum(i=0, n, if(p2=(1-x)*p1-x^2*p0, p0=p1; p1=p2; x^i/p0), x*O(x^n)), n))

Crossrefs

Sequence in context: A107092 A352702 A055588 * A091561 A025265 A152225

Adjacent sequences: A088453 A088454 A088455 * A088457 A088458 A088459

Keyword

nonn

Author

Michael Somos, Oct 01 2003

Status

approved