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A114902 Number of compositions of {1,..,n} such that no two adjacent parts are of equal size (labeled Carlitz compositions).

%I A114902 #12 Sep 21 2019 02:39:12
%S A114902 1,1,1,7,21,81,793,4929,33029,388537,3751311,37585989,523395777,
%T A114902 6814401361,90789460427,1486639926417,24213653736389,403184436319401,
%U A114902 7665459211898263,149067938821523349,2971265450045056871,64800464138121854877,1460876941168812354947
%N A114902 Number of compositions of {1,..,n} such that no two adjacent parts are of equal size (labeled Carlitz compositions).
%H A114902 Alois P. Heinz, <a href="/A114902/b114902.txt">Table of n, a(n) for n = 0..450</a>
%F A114902 a(n) ~ c * d^n * n^(n + 1/2), where d = 0.37565358657373546999489873158654700..., c = 2.0427954030382239202983023897265... - _Vaclav Kotesovec_, Sep 21 2019
%p A114902 b:= proc(n, i) option remember;
%p A114902       `if`(n=0, 1, add(`if`(i=j, 0, b(n-j,
%p A114902       `if`(j>n-j, 0, j)) *binomial(n, j)), j=1..n))
%p A114902     end:
%p A114902 a:= n-> b(n, 0):
%p A114902 seq(a(n), n=0..25);  # _Alois P. Heinz_, Sep 04 2015
%t A114902 b[n_, i_] := b[n, i] = If[n==0, 1, Sum[If[i==j, 0, b[n-j, If[j>n-j, 0, j]]* Binomial[n, j]], {j, 1, n}]]; a[n_] := b[n, 0]; Table[a[n], {n, 0, 25}] (* _Jean-François Alcover_, Feb 20 2017, after _Alois P. Heinz_ *)
%Y A114902 Cf. A000670, A003242, A007837, A032011.
%Y A114902 Column k=1 of A261959.
%K A114902 nonn
%O A114902 0,4
%A A114902 _Christian G. Bower_, Jan 05 2006