cp's OEIS Frontend

A241691 Number of Carlitz compositions of n with exactly one descent.

%I A241691 #8 Apr 27 2014 13:22:58
%S A241691 1,2,4,8,13,21,33,50,73,106,150,209,289,393,529,707,935,1227,1601,
%T A241691 2072,2666,3413,4344,5501,6937,8707,10883,13554,16815,20787,25617,
%U A241691 31465,38532,47056,57302,69596,84320,101907,122875,147833,177471,212608,254201,303335
%N A241691 Number of Carlitz compositions of n with exactly one descent.
%C A241691 No two adjacent parts of a Carlitz composition are equal.
%H A241691 Alois P. Heinz, <a href="/A241691/b241691.txt">Table of n, a(n) for n = 3..1000</a>
%e A241691 a(3) = 1: [2,1].
%e A241691 a(4) = 2: [3,1], [1,2,1].
%e A241691 a(5) = 4: [4,1], [3,2], [2,1,2], [1,3,1].
%e A241691 a(6) = 8: [4,2], [5,1], [3,1,2], [1,3,2], [1,4,1], [2,3,1], [2,1,3], [1,2,1,2].
%e A241691 a(7) = 13: [4,3], [6,1], [5,2], [2,1,4], [4,1,2], [1,4,2], [2,3,2], [3,1,3], [1,5,1], [2,4,1], [1,2,3,1], [1,3,1,2], [1,2,1,3].
%p A241691 b:= proc(n, i) option remember; `if`(n=0, 1,
%p A241691        convert(series(add(`if`(i=j, 0, b(n-j, j)*
%p A241691       `if`(j<i, x, 1)), j=1..n), x, 2), polynom))
%p A241691     end:
%p A241691 a:= n-> coeff(b(n, 0), x, 1):
%p A241691 seq(a(n), n=3..50);
%Y A241691 Column k=1 of A241701.
%K A241691 nonn
%O A241691 3,2
%A A241691 _Alois P. Heinz_, Apr 27 2014