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

0,4

Links

Table of n, a(n) for n=0..35.

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

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).

Example

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 ').

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);

Crossrefs

Cf. A030267, A001870, A129719, A129722.

Sequence in context: A092432 A041669 A300278 * A041089 A042321 A050164

Adjacent sequences: A129717 A129718 A129719 * A129721 A129722 A129723

Keyword

nonn

Author

Emeric Deutsch, May 13 2007

Status

approved