A243121 Number of compositions of n in which the maximal multiplicity of parts equals 4.

1, 0, 5, 5, 21, 40, 100, 210, 396, 870, 1790, 3510, 6681, 13100, 25320, 47835, 87126, 166195, 299375, 542595, 991036, 1775935, 3145270, 5487805, 9852046, 17092310, 29561070, 50696690, 88015196, 150446590, 256066280, 428469220, 727919426, 1224816005, 2043828145

Offset: 4

Author

Alois P. Heinz, May 29 2014

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..1000

Crossrefs

Column k=4 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, 4) -b(n$2, 0, 3):
seq(a(n), n=4..50);

Formula

a(n) = A243082(n) - A232464(n) = A243081(n,4) - A243081(n,3).