A243119 Number of compositions of n in which the maximal multiplicity of parts equals 2.

1, 0, 4, 6, 10, 21, 40, 87, 121, 219, 421, 690, 1159, 1782, 3304, 5190, 8212, 12897, 22084, 33255, 53617, 82539, 124849, 206172, 313339, 472056, 714976, 1077996, 1682806, 2502645, 3804460, 5674305, 8340535, 12245241, 18851899, 27570366, 40385431, 59314572

Offset

2,3

Links

Alois P. Heinz, Table of n, a(n) for n = 2..1000

Formula

a(n) = A232432(n) - A032020(n) = A243081(n,2) - A243081(n,1).

Example

a(6) = 10: [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1], [3,3], [1,1,4], [1,4,1], [4,1,1].

Maple

b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
      add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
    end:
a:= n-> b(n$2, 0, 2) -b(n$2, 0, 1):
seq(a(n), n=2..45);

Crossrefs

Column k=2 of A242447.

Sequence in context: A277455 A320124 A185913 * A277343 A077065 A131867

Adjacent sequences: A243116 A243117 A243118 * A243120 A243121 A243122

Keyword

nonn

Author

Alois P. Heinz, May 29 2014

Status

approved