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A218508 Number of partitions of n in which any two parts differ by at most 6. 4
1, 1, 2, 3, 5, 7, 11, 15, 22, 29, 40, 51, 69, 86, 112, 139, 176, 214, 268, 321, 394, 470, 567, 668, 800, 933, 1103, 1281, 1498, 1725, 2006, 2293, 2643, 3010, 3443, 3897, 4438, 4995, 5652, 6341, 7135, 7967, 8932, 9930, 11079, 12283, 13645, 15071, 16692, 18372 (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..6} (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, 6), 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, 6], {i, 1, n}];

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

CROSSREFS

Column k=6 of A194621.

Sequence in context: A309194 A330640 A319474 * A340719 A026814 A008637

Adjacent sequences:  A218505 A218506 A218507 * A218509 A218510 A218511

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 31 2012

STATUS

approved

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Last modified May 12 21:05 EDT 2021. Contains 343829 sequences. (Running on oeis4.)