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 A049668 a(n) = Fibonacci(8*n)/21. 9
 0, 1, 47, 2208, 103729, 4873055, 228929856, 10754830177, 505248088463, 23735905327584, 1115082302307985, 52385132303147711, 2460986135945634432, 115613963257141670593, 5431395286949712883439, 255159964523379363851040, 11987086937311880388115441 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Colin Barker, Table of n, a(n) for n = 0..500 R. Flórez, R. A. Higuita, A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5 Journal of Integer Sequences, Vol. 17 (2014). Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (47,-1). FORMULA G.f.: x/(1-47*x+x^2), 47=L(8)=A000032(8) (Lucas). a(n) = 47*a(n-1)-a(n-2) ; a(0)=0, a(1)=1. - Philippe Deléham, Nov 18 2008 From Peter Bala, Apr 03 2015: (Start) For integer k, 1 + k*(14 - k)*Sum_{n >= 1} a(n)*x^(2*n) = ( 1 + k/3*Sum_{n >= 1} Fibonacci(4*n)*x^n )*( 1 + k/3*Sum_{n >= 1} Fibonacci(4*n)*(-x)^n ). 1 + 45*Sum_{n >= 1} a(n)*x^(2*n) = ( 1 + Sum_{n >= 1} Lucas(4*n)*x^n )*( 1 + Sum_{n >= 1} Lucas(4*n)*(-x)^n ). 1 - 36*Sum_{n >= 1} a(n)*x^(2*n) = ( 1 + 2*Sum_{n >= 1} Fibonacci(4*n+2)*x^n )*( 1 + 2*Sum_{n >= 1} Fibonacci(4*n+2)*(-x)^n ). (End) a(n) = ((47 + 21*sqrt(5))^(1-n)*(-2^n + (2207 + 987*sqrt(5))^n )) /(2205 + 987*sqrt(5)). - Colin Barker, Jun 03 2016 MATHEMATICA Table[Fibonacci[8*n]/21, {n, 15}] (* Michael De Vlieger, Apr 03 2015 *) PROG (MuPAD) numlib::fibonacci(8*n)/21 \$ n = 0..25; // Zerinvary Lajos, May 09 2008 (PARI) concat(0, Vec(x/(1-47*x+x^2) + O(x^20))) \\ Colin Barker, Jun 03 2016 (PARI) for(n=0, 30, print1(fibonacci(8*n)/21, ", ")) \\ G. C. Greubel, Dec 02 2017 (MAGMA) [Fibonacci(8*n)/21: n in [0..30]]; // G. C. Greubel, Dec 02 2017 CROSSREFS A column of array A028412. Cf. A000045. Sequence in context: A170728 A170766 A218749 * A009991 A052463 A005148 Adjacent sequences:  A049665 A049666 A049667 * A049669 A049670 A049671 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified July 20 04:23 EDT 2018. Contains 312799 sequences. (Running on oeis4.)