OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
EXAMPLE
a(5) = 8: (11111, 11111), (2111, 2111), (2111, 221), (221, 221), (311, 311), (32, 32), (41, 41), (5, 5).
MAPLE
b:= proc(n, m, i) option remember; `if`(n=0,
`if`(m=0, 1, 0), `if`(i<1, 0, b(n, m, i-1)+add(add(
b(sort([n-i*j, m-i*h])[], i-1), h=1..m/i), j=1..n/i)))
end:
a:= n-> (b(n$3)+combinat[numbpart](n))/2:
seq(a(n), n=0..50);
MATHEMATICA
b[n_, m_, i_] := b[n, m, i] = If[n == 0, If[m == 0, 1, 0], If[i < 1, 0, b[n, m, i-1] + Sum[Sum[b[Sequence @@ Sort[{n-i*j, m-i*h}], i-1], {h, 1, m/i}], {j, 1, n/i}]]];
a[n_] := (b[n, n, n] + PartitionsP[n])/2;
Table[a[n], {n, 0, 50}] (* Jean-François Alcover, Feb 29 2024, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 29 2024
STATUS
approved