OFFSET
0,3
LINKS
Chai Wah Wu, Table of n, a(n) for n = 0..142 (n = 0..100 from Alois P. Heinz)
EXAMPLE
a(4) = 3: 211, 121, 112.
a(5) = 12: 23, 32, 113, 122, 131, 212, 221, 311, 1112, 1121, 1211, 2111.
MAPLE
b:= proc(n, i, s, p) option remember;
`if`(n=0, `if`(s={$0..max(s)}, p!, 0), `if`(i<1, 0, add(
b(n-i*j, i-1, {s[], j, `if`(j=0, 0, i)}, p+j)/j!, j=0..n/i)))
end:
a:= n-> b(n, floor((sqrt(1+8*(n+1))-1)/2), {0}, 0):
seq(a(n), n=0..35);
MATHEMATICA
b[n_, i_, s_, p_] := b[n, i, s, p] =
If[n == 0, If[s == Range[0, Max[s]], p!, 0], If[i < 1, 0, Sum[
b[n - i*j, i - 1, Union@Flatten@{s, j, If[j == 0, 0, i]}, p + j]/j!,
{j, 0, n/i}]]];
a[n_] := b[n, Floor[(Sqrt[1 + 8*(n + 1)] - 1)/2], {0}, 0];
Table[a[n], {n, 0, 35}] (* Jean-François Alcover, May 30 2022, after Alois P. Heinz *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Jun 30 2020
STATUS
approved