A243737 Number of compositions of n with exactly two occurrences of the largest part.

1, 0, 1, 3, 7, 13, 25, 46, 89, 175, 351, 710, 1443, 2926, 5920, 11936, 23987, 48072, 96139, 191977, 382992, 763686, 1522581, 3035979, 6055454, 12082887, 24120923, 48174935, 96259627, 192418152, 384772810, 769651514, 1539889604, 3081525905, 6167365392

Offset

2,4

Links

Joerg Arndt and Alois P. Heinz, Table of n, a(n) for n = 2..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:=2;
      add(b(n-i*k, k, i-1)/k!, i=1..n/k)
    end:
seq(a(n), n=2..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=2; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]) ; Table[ a[n], {n, 2, 40}] (* Jean-François Alcover, Feb 10 2015, after Maple *)

Crossrefs

Column k=2 of A238341.

Sequence in context: A210613 A363707 A304648 * A269832 A341579 A336726

Adjacent sequences: A243734 A243735 A243736 * A243738 A243739 A243740

Keyword

nonn

Author

Joerg Arndt and Alois P. Heinz, Jun 09 2014

Status

approved