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 A176281 Hankel transform of A176280. 2
 1, 3, 12, 56, 280, 1440, 7488, 39104, 204544, 1070592, 5604864, 29345792, 153653248, 804532224, 4212572160, 22057287680, 115493404672, 604731211776, 3166413520896, 16579556016128, 86811681488896, 454551863820288 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (8,-16,8). FORMULA G.f.: (1-5*x+4*x^2)/(1-8*x+16*x^2-8*x^3) = (1-5*x+4*x^2)/((1-2*x)*(1-6*x+4*x^2)). a(n) = 2^(n-1) + (3-sqrt(5))^n*((5-sqrt(5))/20) + (3+sqrt(5))^n*((5+sqrt(5))/20). a(n) = 2^(n-1) + A082761(n)/2. - R. J. Mathar, Sep 30 2012 a(0)=1, a(1)=3, a(2)=12, a(n) = 8*a(n-1) - 16*a(n-2) + 8*a(n-3). - Harvey P. Dale, Aug 14 2013 a(n) = 2^(n-1)*(Fibonacci(2*n+1) + 1). - G. C. Greubel, Nov 24 2019 MAPLE with(combinat); seq(2^(n-1)*(fibonacci(2*n+1) + 1), n=0..30); # G. C. Greubel, Nov 24 2019 MATHEMATICA CoefficientList[Series[(1-5x+4x^2)/((1-2x)(1-6x+4x^2)), {x, 0, 40}], x] (* or *) LinearRecurrence[{8, -16, 8}, {1, 3, 12}, 40] (* Harvey P. Dale, Aug 14 2013 *) PROG (PARI) vector(31, n, 2^(n-2)*(fibonacci(2*n-1) + 1)) \\ G. C. Greubel, Nov 24 2019 (MAGMA) [2^(n-1)*(Fibonacci(2*n+1) + 1): n in [0..30]]; G. C. Greubel, Nov 24 2019 (Sage) [2^(n-1)*(fibonacci(2*n+1) + 1) for n in (0..30)] # G. C. Greubel, Nov 24 2019 (GAP) List([0..30], n-> 2^(n-1)*(Fibonacci(2*n+1) + 1)); # G. C. Greubel, Nov 24 2019 CROSSREFS Cf. A000045. Sequence in context: A185630 A284843 A107318 * A050147 A259800 A120921 Adjacent sequences:  A176278 A176279 A176280 * A176282 A176283 A176284 KEYWORD easy,nonn AUTHOR Paul Barry, Apr 14 2010 STATUS approved

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Last modified June 1 04:37 EDT 2020. Contains 334758 sequences. (Running on oeis4.)