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

%I A243121 #7 May 29 2014 18:48:39
%S A243121 1,0,5,5,21,40,100,210,396,870,1790,3510,6681,13100,25320,47835,87126,
%T A243121 166195,299375,542595,991036,1775935,3145270,5487805,9852046,17092310,
%U A243121 29561070,50696690,88015196,150446590,256066280,428469220,727919426,1224816005,2043828145
%N A243121 Number of compositions of n in which the maximal multiplicity of parts equals 4.
%H A243121 Alois P. Heinz, <a href="/A243121/b243121.txt">Table of n, a(n) for n = 4..1000</a>
%F A243121 a(n) = A243082(n) - A232464(n) = A243081(n,4) - A243081(n,3).
%p A243121 b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p A243121       add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
%p A243121     end:
%p A243121 a:= n-> b(n$2, 0, 4) -b(n$2, 0, 3):
%p A243121 seq(a(n), n=4..50);
%Y A243121 Column k=4 of A242447.
%K A243121 nonn
%O A243121 4,3
%A A243121 _Alois P. Heinz_, May 29 2014