%I #6 Apr 28 2014 09:26:12
%S 13,81,336,1151,3437,9286,23271,54846,122857,263680,545412,1092394,
%T 2126688,4036767,7490050,13614573,24287970,42592752,73525406,
%U 125089010,209962350,348026885,570159824,923885796,1481735623,2353522164,3704254256,5780115565,8945915366
%N Number of Carlitz compositions of n with exactly six descents.
%C No two adjacent parts of a Carlitz composition are equal.
%H Alois P. Heinz, <a href="/A241696/b241696.txt">Table of n, a(n) for n = 18..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, 7), polynom))
%p end:
%p a:= n-> coeff(b(n, 0), x, 6):
%p seq(a(n), n=18..50);
%Y Column k=6 of A241701.
%K nonn
%O 18,1
%A _Alois P. Heinz_, Apr 27 2014