login
Number of compositions of n in which the maximal multiplicity of parts equals 4.
2

%I #7 May 29 2014 18:48:39

%S 1,0,5,5,21,40,100,210,396,870,1790,3510,6681,13100,25320,47835,87126,

%T 166195,299375,542595,991036,1775935,3145270,5487805,9852046,17092310,

%U 29561070,50696690,88015196,150446590,256066280,428469220,727919426,1224816005,2043828145

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

%H Alois P. Heinz, <a href="/A243121/b243121.txt">Table of n, a(n) for n = 4..1000</a>

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

%p b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,

%p add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))

%p end:

%p a:= n-> b(n$2, 0, 4) -b(n$2, 0, 3):

%p seq(a(n), n=4..50);

%Y Column k=4 of A242447.

%K nonn

%O 4,3

%A _Alois P. Heinz_, May 29 2014