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A243120 Number of compositions of n in which the maximal multiplicity of parts equals 3.

%I A243120 #6 May 29 2014 18:45:48
%S A243120 1,0,4,5,18,34,59,132,272,519,966,1746,3487,5986,10570,19701,34444,
%T A243120 59250,101155,180588,302788,515205,841042,1449392,2420163,3959442,
%U A243120 6472636,10656987,17332640,28234296,45337971,72306544,117761744,185704091,295918788,466574348
%N A243120 Number of compositions of n in which the maximal multiplicity of parts equals 3.
%H A243120 Alois P. Heinz, <a href="/A243120/b243120.txt">Table of n, a(n) for n = 3..1000</a>
%F A243120 a(n) = A232464(n) - A232432(n) = A243081(n,3) - A243081(n,2).
%p A243120 b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p A243120       add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
%p A243120     end:
%p A243120 a:= n-> b(n$2, 0, 3) -b(n$2, 0, 2):
%p A243120 seq(a(n), n=3..50);
%Y A243120 Column k=3 of A242447.
%K A243120 nonn
%O A243120 3,3
%A A243120 _Alois P. Heinz_, May 29 2014