OFFSET
0,5
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..350
EXAMPLE
a(5) = 6: (2111, 11111), (2111, 221), (221, 11111), (221, 2111), (311, 11111), (41, 11111).
a(6) = 17: (21111, 111111), (21111, 2211), (21111, 222), (2211, 111111), (2211, 21111), (2211, 222), (3111, 111111), (321, 111111), (321, 21111), (321, 2211), (321, 222), (321, 3111), (3111, 33), (321, 33), (411, 111111), (42, 222), (51, 111111).
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(n-i*j, m-i*h, i-1), h=0..m/i), j=1..n/i)))
end:
a:= n-> b(n$3)-combinat[numbpart](n):
seq(a(n), n=0..42);
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[n - i*j, m - i*h, i - 1], {h, 0, m/i}], {j, 1, n/i}]]];
a[n_] := b[n, n, n] - PartitionsP[n];
Table[a[n], {n, 0, 42}] (* Jean-François Alcover, Feb 29 2024, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jan 29 2024
STATUS
approved