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 A056236 a(n) = (2 + sqrt(2))^n + (2 - sqrt(2))^n. 10
 2, 4, 12, 40, 136, 464, 1584, 5408, 18464, 63040, 215232, 734848, 2508928, 8566016, 29246208, 99852800, 340918784, 1163969536, 3974040576, 13568223232, 46324811776, 158162800640, 540001579008, 1843680714752, 6294719700992 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS First differences give A060995. - Jeremy Gardiner, Aug 11 2013 Binomial transform of A002203 [Bhadouria]. The binomial transform of this sequence is 2, 6, 22, 90, 386, .. = 2*A083878(n). - R. J. Mathar, Nov 10 2013 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 P. Bhadouria, D. Jhala, and B. Singh, Binomial Transforms of the k-Lucas Sequences and its Properties, The Journal of Mathematics and Computer Science (JMCS), Volume 8, Issue 1, Pages 81-92, sequence B_2. Takao Komatsu, Asymmetric Circular Graph with Hosoya Index and Negative Continued Fractions, arXiv:2105.08277 [math.CO], 2021. Youngwoo Kwon, Binomial transforms of the modified k-Fibonacci-like sequence, arXiv:1804.08119 [math.NT], 2018. Index entries for linear recurrences with constant coefficients, signature (4,-2). FORMULA a(n) = 4*a(n-1) - 2*a(n-2). a(n) = a(n-2) - a(n-1) + 2*A020727(n-1). a(n) = 2*A006012(n) = 4*A007052(n-1). For n>2, a(n) = floor((2+sqrt(2))*a(n-1)). G.f.: 2*(1-2*x)/(1-4*x+2*x^2). From L. Edson Jeffery, Apr 08 2011: (Start) a(n) = 2^(2*n)*(cos(Pi/8)^(2*n) + cos(3*Pi/8)^(2*n)). a(n) = 3*a(n-1) + Sum_{k=1..(n-2)} a(k), for n>1, with a(0)=2, a(1)=4. (End) a(n) = [x^n] ( (1 + 4*x + sqrt(1 + 8*x + 8*x^2))/2 )^n for n >= 1. - Peter Bala, Jun 23 2015 MATHEMATICA LinearRecurrence[{4, -2}, {2, 4}, 30] (* Harvey P. Dale, Jan 18 2013 *) PROG (PARI) a(n) = 2*real((2+quadgen(8))^n); (Sage) [lucas_number2(n, 4, 2) for n in range(37)] # Zerinvary Lajos, Jun 25 2008 CROSSREFS Cf. A006012, A007052, A020727. Sequence in context: A113179 A214761 A327845 * A300652 A028329 A204678 Adjacent sequences: A056233 A056234 A056235 * A056237 A056238 A056239 KEYWORD nonn,easy AUTHOR Henry Bottomley, Aug 11 2000 EXTENSIONS More terms from James A. Sellers, Aug 25 2000 STATUS approved

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Last modified November 30 01:30 EST 2023. Contains 367452 sequences. (Running on oeis4.)