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A243119 Number of compositions of n in which the maximal multiplicity of parts equals 2.

%I A243119 #10 May 29 2014 18:47:08
%S A243119 1,0,4,6,10,21,40,87,121,219,421,690,1159,1782,3304,5190,8212,12897,
%T A243119 22084,33255,53617,82539,124849,206172,313339,472056,714976,1077996,
%U A243119 1682806,2502645,3804460,5674305,8340535,12245241,18851899,27570366,40385431,59314572
%N A243119 Number of compositions of n in which the maximal multiplicity of parts equals 2.
%H A243119 Alois P. Heinz, <a href="/A243119/b243119.txt">Table of n, a(n) for n = 2..1000</a>
%F A243119 a(n) = A232432(n) - A032020(n) = A243081(n,2) - A243081(n,1).
%e A243119 a(6) = 10: [1,1,2,2], [1,2,1,2], [1,2,2,1], [2,1,1,2], [2,1,2,1], [2,2,1,1], [3,3], [1,1,4], [1,4,1], [4,1,1].
%p A243119 b:= proc(n, i, p, k) option remember; `if`(n=0, p!, `if`(i<1, 0,
%p A243119       add(b(n-i*j, i-1, p+j, k)/j!, j=0..min(n/i, k))))
%p A243119     end:
%p A243119 a:= n-> b(n$2, 0, 2) -b(n$2, 0, 1):
%p A243119 seq(a(n), n=2..45);
%Y A243119 Column k=2 of A242447.
%K A243119 nonn
%O A243119 2,3
%A A243119 _Alois P. Heinz_, May 29 2014