cp's OEIS Frontend

A130138 Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 1011's (n>=0, 0<=k<=floor((n-1)/3)). A Fibonacci binary word is a binary word having no 00 subword.

%I A130138 #5 Sep 03 2013 10:38:38
%S A130138 1,2,3,5,7,1,9,4,11,10,13,20,1,15,35,5,17,56,16,19,84,40,1,21,120,86,
%T A130138 6,23,165,166,23,25,220,296,68,1,27,286,496,171,7,29,364,791,382,31,
%U A130138 31,455,1211,781,105,1,33,560,1792,1488,300,8,35,680,2576,2678,756,40,37
%N A130138 Triangle read by rows: T(n,k) is the number of Fibonacci binary words of length n and having k 1011's (n>=0, 0<=k<=floor((n-1)/3)). A Fibonacci binary word is a binary word having no 00 subword.
%C A130138 Row n has 1+floor((n-1)/3) terms. Row sums are the Fibonacci numbers (A000045). T(n,0)=A004280(n+1). Sum(k*T(n,k), k>=0)=A004798(n-3) (n>=4).
%F A130138 G.f.=G(t,z)=(1+z)(1+z^3-tz^3)/[1-z-z^2+z^3-tz^3].
%e A130138 T(7,2)=1 because we have 1011011.
%e A130138 Triangle starts:
%e A130138 1;
%e A130138 2;
%e A130138 3;
%e A130138 5;
%e A130138 7,1;
%e A130138 9,4;
%e A130138 11,10;
%e A130138 13,20,1;
%e A130138 15,35,5;
%p A130138 G:=(1+z)*(1+z^3-t*z^3)/(1-z-z^2+z^3-t*z^3): Gser:=simplify(series(G,z=0,24)): for n from 0 to 21 do P[n]:=sort(coeff(Gser,z,n)) od: 1; for n from 1 to 21 do seq(coeff(P[n],t,j),j=0..floor((n-1)/3)) od; # yields sequence in triangular form
%Y A130138 Cf. A000045, A004280, A004798.
%K A130138 nonn,tabf
%O A130138 0,2
%A A130138 _Emeric Deutsch_, May 13 2007