A218510 Number of partitions of n in which any two parts differ by at most 8.

1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 55, 75, 96, 127, 161, 208, 260, 330, 407, 509, 621, 765, 925, 1127, 1350, 1627, 1934, 2310, 2725, 3227, 3782, 4446, 5178, 6044, 7000, 8122, 9355, 10791, 12370, 14195, 16196, 18494, 21012, 23887, 27029, 30596, 34492, 38894

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: 1 + Sum_{j>0} x^j / Product_{i=0..8} (1-x^(i+j)).

Maple

b:= proc(n, i, k) option remember; `if`(n<0 or k<0, 0,
      `if`(n=0, 1, `if`(i<1, 0, b(n, i-1, k-1) +b(n-i, i, k))))
    end:
a:= n-> `if`(n=0, 1, 0) +add(b(n-i, i, 8), i=1..n):
seq(a(n), n=0..80);

Mathematica

b[n_, i_, k_] := b[n, i, k] = If[n < 0 || k < 0, 0, If[n == 0, 1, If[i < 1, 0, b[n, i - 1, k - 1] + b[n - i, i, k]]]];
a[n_] := If[n == 0, 1, 0] + Sum[b[n - i, i, 8], {i, 1, n}];
Table[a[n], {n, 0, 80}] (* Jean-François Alcover, May 20 2018, after Alois P. Heinz *)

Crossrefs

Column k=8 of A194621.

Sequence in context: A184645 A053691 A242696 * A026816 A008639 A341914

Adjacent sequences: A218507 A218508 A218509 * A218511 A218512 A218513

Keyword

nonn

Author

Alois P. Heinz, Oct 31 2012

Status

approved