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A218511 Number of partitions of n in which any two parts differ by at most 9. 4
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 42, 56, 76, 99, 130, 168, 216, 274, 348, 435, 544, 674, 831, 1017, 1244, 1507, 1823, 2193, 2629, 3136, 3734, 4420, 5223, 6148, 7215, 8438, 9850, 11453, 13292, 15382, 17758, 20447, 23502, 26935, 30818, 35181, 40082, 45570 (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..9} (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, 9), 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, 9], {i, 1, n}];

Table[a[n], {n, 0, 80}] (* Jean-Fran├žois Alcover, May 20 2018, after Alois P. Heinz *)

CROSSREFS

Column k=9 of A194621.

Sequence in context: A036010 A328545 A192061 * A008640 A008634 A238869

Adjacent sequences:  A218508 A218509 A218510 * A218512 A218513 A218514

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 31 2012

STATUS

approved

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Last modified May 16 11:20 EDT 2021. Contains 343942 sequences. (Running on oeis4.)