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A241693 Number of Carlitz compositions of n with exactly three descents.

%I A241693 #6 Apr 28 2014 09:31:48
%S A241693 3,11,31,78,175,363,715,1342,2421,4237,7208,11971,19473,31083,48787,
%T A241693 75437,115046,173263,257972,380039,554400,801452,1148805,1633699,
%U A241693 2306108,3232635,4501745,6230400,8572442,11729536,15965001,21621202,29141879,39100192,52233835
%N A241693 Number of Carlitz compositions of n with exactly three descents.
%C A241693 No two adjacent parts of a Carlitz composition are equal.
%H A241693 Alois P. Heinz, <a href="/A241693/b241693.txt">Table of n, a(n) for n = 9..1000</a>
%p A241693 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A241693        convert(series(add(`if`(i=j, 0, b(n-j, j)*
%p A241693       `if`(j<i, x, 1)), j=1..n), x, 4), polynom))
%p A241693     end:
%p A241693 a:= n-> coeff(b(n, 0), x, 3):
%p A241693 seq(a(n), n=9..50);
%Y A241693 Column k=3 of A241701.
%K A241693 nonn
%O A241693 9,1
%A A241693 _Alois P. Heinz_, Apr 27 2014