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Number of Carlitz compositions of n with exactly two descents.
2

%I #6 Apr 28 2014 09:33:19

%S 2,5,12,27,53,98,174,296,486,781,1222,1874,2827,4195,6138,8873,12675,

%T 17918,25095,34832,47954,65529,88911,119842,160552,213841,283266,

%U 373318,489601,639149,830750,1075292,1386313,1780572,2278703,2906137,3694123,4680892

%N Number of Carlitz compositions of n with exactly two descents.

%C No two adjacent parts of a Carlitz composition are equal.

%H Alois P. Heinz, <a href="/A241692/b241692.txt">Table of n, a(n) for n = 6..1000</a>

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

%p convert(series(add(`if`(i=j, 0, b(n-j, j)*

%p `if`(j<i, x, 1)), j=1..n), x, 3), polynom))

%p end:

%p a:= n-> coeff(b(n, 0), x, 2):

%p seq(a(n), n=6..50);

%Y Column k=2 of A241701.

%K nonn

%O 6,1

%A _Alois P. Heinz_, Apr 27 2014