A129720 Number of 0's in odd position in all Fibonacci binary words of length n. A Fibonacci binary word is a binary word having no 00 subword.

0, 1, 1, 4, 5, 14, 19, 46, 65, 145, 210, 444, 654, 1331, 1985, 3926, 5911, 11434, 17345, 32960, 50305, 94211, 144516, 267384, 411900, 754309, 1166209, 2116936, 3283145, 5914310, 9197455, 16458034, 25655489, 45638101, 71293590, 126159156

Offset: 0

Author

Emeric Deutsch, May 13 2007

Keywords

• nonn

Examples

			a(4)=5 because in 1110, 1111, 110'1, 1010, 1011, 0'110, 0'111 and 0'10'1 one has altogether five 0's in odd position (marked by ').
		

Links

• É. Czabarka, R. Flórez, L. Junes, A Discrete Convolution on the Generalized Hosoya Triangle, Journal of Integer Sequences, 18 (2015), #15.1.6.

Crossrefs

Cf. A030267, A001870, A129719, A129722.

Programs

Maple

g:=z*(1-z^2)/(1-z-z^2)^2/(1+z-z^2): gser:=series(g,z=0,43): seq(coeff(gser,z,n),n=0..40);

Formula

G.f.: z(1-z^2)/((1-z-z^2)^2*(1+z-z^2)).

a(2n) = a(2n-1) + a(2n-2) (n >= 1).

a(2n-1) = A030267(n).

a(2n) = A129722(2n) = A001870(n-1).

a(n) = Sum_{k=0..ceiling(n/2)} k*A129719(n,k).