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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
OFFSET
0,3
LINKS
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-François Alcover, May 20 2018, after Alois P. Heinz *)
CROSSREFS
Column k=7 of A194621.
Sequence in context: A209039 A182805 A309058 * A026815 A341913 A008638
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 31 2012
STATUS
approved