A218512 Number of partitions of n in which any two parts differ by at most 10.

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

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-François 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