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 A102902 a(n) = 9*a(n-1) - 16*a(n-2), with a(0) = 1, a(1) = 9. 1
 1, 9, 65, 441, 2929, 19305, 126881, 833049, 5467345, 35877321, 235418369, 1544728185, 10135859761, 66507086889, 436390025825, 2863396842201, 18788331166609, 123280631024265, 808912380552641, 5307721328585529 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Indranil Ghosh, Table of n, a(n) for n = 0..1221 R. Flórez, R. A. Higuita, and A. Mukherjee, Alternating Sums in the Hosoya Polynomial Triangle, Article 14.9.5, Journal of Integer Sequences, Vol. 17 (2014). Index entries for linear recurrences with constant coefficients, signature (9,-16). FORMULA G.f.: 1/(1-9*x+16*x^2). a(n) = Sum_{k=0..n} binomial(2*n-k+1, k)*4^k. a(n) = Sum_{k=0..floor(n/2)} binomial(n-k, k)*(-16)^k*9^(n-2*k). a(n) = (1/sqrt(17))*( ((9+sqrt(17))/2)^(n+1) - ((9-sqrt(17))/2)^(n+1) ), with n >= 0. - Paolo P. Lava, Jun 16 2008 a(n) = 4^n * ChebyshevU(n, 9/8). - G. C. Greubel, Dec 09 2022 MATHEMATICA LinearRecurrence[{9, -16}, {1, 9}, 20] (* Harvey P. Dale, Jul 28 2016 *) PROG (SageMath) [lucas_number1(n, 9, 16) for n in range(1, 21)] # Zerinvary Lajos, Apr 23 2009 (Magma) [4^n*Evaluate(ChebyshevSecond(n+1), 9/8): n in [0..30]]; // G. C. Greubel, Dec 09 2022 CROSSREFS Cf. A002540, A099459. Sequence in context: A055284 A351530 A081040 * A127534 A037548 A238275 Adjacent sequences: A102899 A102900 A102901 * A102903 A102904 A102905 KEYWORD easy,nonn AUTHOR Paul Barry, Jan 17 2005 STATUS approved

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Last modified September 22 17:32 EDT 2023. Contains 365531 sequences. (Running on oeis4.)