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 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. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS 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

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Last modified January 23 03:02 EST 2021. Contains 340384 sequences. (Running on oeis4.)