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

3,5

Links

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

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 *)

Crossrefs

Column k=3 of A238341.

Sequence in context: A085360 A265050 A376712 * A258352 A024988 A301174

Adjacent sequences: A243735 A243736 A243737 * A243739 A243740 A243741

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved