A243119 - OEIS

%I #10 May 29 2014 18:47:08

%S 1,0,4,6,10,21,40,87,121,219,421,690,1159,1782,3304,5190,8212,12897,

%T 22084,33255,53617,82539,124849,206172,313339,472056,714976,1077996,

%U 1682806,2502645,3804460,5674305,8340535,12245241,18851899,27570366,40385431,59314572

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

%H Alois P. Heinz, <a href="/A243119/b243119.txt">Table of n, a(n) for n = 2..1000</a>

%F a(n) = A232432(n) - A032020(n) = A243081(n,2) - A243081(n,1).

%e 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 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, 2) -b(n$2, 0, 1):

%p seq(a(n), n=2..45);

%Y Column k=2 of A242447.

%K nonn

%O 2,3

%A _Alois P. Heinz_, May 29 2014