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A218509 Number of partitions of n in which any two parts differ by at most 7. 4
1, 1, 2, 3, 5, 7, 11, 15, 22, 30, 41, 54, 72, 93, 120, 153, 194, 242, 302, 372, 457, 556, 675, 812, 975, 1162, 1381, 1632, 1923, 2254, 2636, 3068, 3562, 4119, 4752, 5462, 6265, 7162, 8170, 9293, 10549, 11942, 13495, 15211, 17115, 19214, 21534, 24083, 26892 (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..7} (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, 7), 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, 7], {i, 1, n}];

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

CROSSREFS

Column k=7 of A194621.

Sequence in context: A209039 A182805 A309058 * A026815 A341913 A008638

Adjacent sequences:  A218506 A218507 A218508 * A218510 A218511 A218512

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Oct 31 2012

STATUS

approved

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Last modified May 13 18:37 EDT 2021. Contains 343868 sequences. (Running on oeis4.)