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A218512 Number of partitions of n in which any two parts differ by at most 10. 3
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 77, 100, 133, 171, 223, 282, 362, 453, 572, 709, 884, 1084, 1337, 1626, 1984, 2394, 2896, 3468, 4162, 4951, 5897, 6972, 8249, 9696, 11402, 13330, 15586, 18131, 21090, 24417, 28264, 32580, 37541, 43097, 49449, 56544 (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..10} (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, 10), 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, 10], {i, 1, n}];

Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, May 21 2018, translated from Maple *)

CROSSREFS

Column k=10 of A194621.

Sequence in context: A104501 A328546 A242697 * A008635 A008641 A341714

Adjacent sequences:  A218509 A218510 A218511 * A218513 A218514 A218515

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 31 2012

STATUS

approved

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Last modified May 12 10:17 EDT 2021. Contains 343821 sequences. (Running on oeis4.)