OFFSET
1,8
FORMULA
G.f.: Sum_{k>=1} x^(6*k)/Product_{j>=k} (1-x^j).
MAPLE
b:= proc(n, i) option remember; `if`(n=0, 1,
`if`(i>n, 0, b(n, i+1)+b(n-i, i)))
end:
a:= n-> add(b(n-6*i, i), i=1..n/6):
seq(a(n), n=1..60); # Alois P. Heinz, May 17 2023
MATHEMATICA
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i > n, 0, b[n, i+1] + b[n-i, i]]];
a[n_] := Sum[b[n - 6 i, i], {i, 1, n/6}];
Array[a, 60] (* Jean-François Alcover, May 30 2024, after Alois P. Heinz *)
PROG
(PARI) my(N=60, x='x+O('x^N)); concat([0, 0, 0, 0, 0], Vec(sum(k=1, N, x^(6*k)/prod(j=k, N, 1-x^j))))
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, May 17 2023
STATUS
approved