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-François Alcover, May 20 2018, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 31 2012
STATUS
approved