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 A130567 Expansion of x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)). 0
 2, 7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623, 4198399, 16785407, 67125247, 268468223, 1073807359, 4295098367, 17180131327, 68720001023, 274878955519, 1099513724927, 4398050705407, 17592194433023, 70368760954879 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS A. M. Cohen and D. E. Taylor, On a Certain Lie Algebra Defined by a Finite Group, American Math Monthly, volume 114, Number 7, Aug-Sept 2007, pages 633-638. FORMULA a(n) = 2^(2*n - 1) + 2*a(n - 1) + 1. From R. J. Mathar, Jun 13 2008: (Start) O.g.f.: x*(2 - 7*x + 2*x^2)/((1-x)*(1-4*x)*(1-2*x)). a(n) = A093069(n-2), n>1. (End) a(n) = -1 + 2*2^n + 4^n, with n>=0. - Paolo P. Lava, Jul 30 2008 MATHEMATICA f[n_Integer?Positive] := f[n] = 2^(2*n - 1) + 2*f[n - 1] + 1; f[0] = 2; Table[f[n], {n, 0, 30}] CoefficientList[Series[x*(2-7x+2x^2)/((1-x)(1-4x)(1-2x)), {x, 0, 30}], x] (* Harvey P. Dale, Sep 07 2015 *) CROSSREFS Cf. A099393, A028244. Sequence in context: A198944 A112657 A007717 * A091514 A143629 A176287 Adjacent sequences:  A130564 A130565 A130566 * A130568 A130569 A130570 KEYWORD nonn,easy AUTHOR Roger L. Bagula, Aug 09 2007 EXTENSIONS New name from Joerg Arndt, Feb 08 2015 STATUS approved

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