OFFSET
0,4
COMMENTS
Number of partitions of n such that if k is the least part, then k occurs at least k times. - Joerg Arndt, Apr 17 2011
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
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-> `if`(n=0, 1, add(b(n-j^2, j), j=1..isqrt(n))):
seq(a(n), n=0..50); # Alois P. Heinz, Jan 03 2021
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_] := If[n==0, 1, Sum[b[n - j^2, j], {j, 1, Sqrt[n]}]];
a /@ Range[0, 50] (* Jean-François Alcover, Jan 25 2021, after Alois P. Heinz *)
PROG
(PARI) N=55; x='x+O('x^N);
t=1+sum(n=1, N, x^(n^2)/prod(k=n, N, 1-x^k));
Vec(t)
CROSSREFS
KEYWORD
nonn
AUTHOR
Joerg Arndt, Mar 24 2011
STATUS
approved