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 A152035 Expansion of g.f. (1-2*x^2)/(1-2*x-2*x^2). 3
 1, 2, 4, 12, 32, 88, 240, 656, 1792, 4896, 13376, 36544, 99840, 272768, 745216, 2035968, 5562368, 15196672, 41518080, 113429504, 309895168, 846649344, 2313089024, 6319476736, 17265131520, 47169216512, 128868696064, 352075825152, 961889042432, 2627929735168, 7179637555200, 19615134580736 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Essentially same as A028860. - Philippe Deléham, Sep 21 2009 LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (2,2). FORMULA a(n) = 2*(a(n-1) + a(n-2)) for n >= 3. - Peter Luschny, Jan 03 2019 MAPLE a := proc(n) option remember; `if`(n < 3, [1, 2, 4][n+1], 2*(a(n-1) + a(n-2))) end: seq(a(n), n=0..31); # Peter Luschny, Jan 03 2019 MATHEMATICA f[n_] = 2^n*Product[(1 + 2*Cos[k*Pi/n]^2), {k, 1, Floor[(n - 1)/2]}]; Table[FullSimplify[ExpandAll[f[n]]], {n, 0, 15}] CoefficientList[Series[(1-2x^2)/(1-2x-2x^2), {x, 0, 40}], x] (* Harvey P. Dale, Sep 23 2014 *) LinearRecurrence[{2, 2}, {1, 2, 4}, 40] (* Harvey P. Dale, May 12 2023 *) PROG (Magma) [1] cat [n le 2 select 2^n else 2*(Self(n-1) +Self(n-2)): n in [1..30]]; // G. C. Greubel, Sep 20 2023 (SageMath) @CachedFunction def a(n): # a = A152035 if n<3: return (1, 2, 4)[n] else: return 2*(a(n-1) + a(n-2)) [a(n) for n in range(31)] # G. C. Greubel, Sep 20 2023 CROSSREFS Cf. A028860. Row sums of A322942. Sequence in context: A181329 A293007 A028860 * A026151 A025178 A231295 Adjacent sequences: A152032 A152033 A152034 * A152036 A152037 A152038 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Nov 20 2008 EXTENSIONS Edited by N. J. A. Sloane, Apr 11 2009, based on comments from Philippe Deléham and R. J. Mathar More terms from Philippe Deléham, Sep 21 2009 STATUS approved

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Last modified June 14 02:27 EDT 2024. Contains 373392 sequences. (Running on oeis4.)