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A218510 Number of partitions of n in which any two parts differ by at most 8. 4
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, May 20 2018, after Alois P. Heinz *)

CROSSREFS

Column k=8 of A194621.

Sequence in context: A184645 A053691 A242696 * A026816 A008639 A008633

Adjacent sequences:  A218507 A218508 A218509 * A218511 A218512 A218513

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 31 2012

STATUS

approved

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Last modified November 22 16:26 EST 2019. Contains 329396 sequences. (Running on oeis4.)