A243121 - OEIS

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

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OFFSET

4,3

LINKS

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

FORMULA

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

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):