A243741 Number of compositions of n with exactly six occurrences of the largest part.

1, 0, 0, 0, 0, 0, 1, 7, 28, 84, 210, 462, 925, 1723, 3038, 5145, 8498, 13930, 23143, 39859, 72500, 140266, 286678, 609217, 1323197, 2897511, 6339636, 13787488, 29726648, 63472185, 134190162, 280988786, 583076160, 1199816068, 2449963412, 4967798570, 10009806563

Offset

6,8

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 6..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:=6;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=6..50);

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=6; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 6, 40}] (* Jean-François Alcover, Feb 10 2015, after Maple *)

Crossrefs

Column k=6 of A238341.

Sequence in context: A049017 A019501 A229887 * A369809 A145456 A369808

Adjacent sequences: A243738 A243739 A243740 * A243742 A243743 A243744

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved