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

Author

Alois P. Heinz, May 29 2014

Keywords

• nonn

Examples

			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].
		

Links

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

Crossrefs

Column k=2 of A242447.

Programs

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);

Formula

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