A243738 Number of compositions of n with exactly three occurrences of the largest part.

1, 0, 0, 1, 4, 10, 21, 39, 70, 125, 229, 435, 859, 1739, 3574, 7384, 15239, 31312, 63968, 129898, 262316, 527169, 1055254, 2105849, 4192933, 8335832, 16557580, 32877010, 65286137, 129695835, 257817166, 512918318, 1021351641, 2035674817, 4061093104, 8108844651

Offset: 3

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Keywords

• nonn

Links

• Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 3..650

Crossrefs

Column k=3 of A238341.

Programs

Maple

b:= proc(n, p, i) option remember; `if`(n=0, p!,
      `if`(i<1, 0, add(b(n-i*j, p+j, i-1)/j!, j=0..n/i)))
    end:
a:= proc(n) local k; k:=3;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=3..40);

Mathematica

b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_] := (k=3; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Feb 10 2015, after Maple *)