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 A121990 Expansion of x*(1+9*x+2*x^2)/((1-x)*(x^2-3*x+1)). 1
 1, 13, 50, 149, 409, 1090, 2873, 7541, 19762, 51757, 135521, 354818, 928945, 2432029, 6367154, 16669445, 43641193, 114254146, 299121257, 783109637, 2050207666, 5367513373, 14052332465, 36789484034, 96316119649, 252158874925 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS G. C. Greubel, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (4,-4,1). FORMULA a(n) = 3*a(n - 1) - a(n - 2) + 12. a(n) = (1/10)*(-120 + (65 - 11*sqrt(5))*((1/2)*(3 - sqrt(5)))^n + ((1/2)*(3 + sqrt(5)))^n*(65 + 11*sqrt(5))). From R. J. Mathar, Apr 04 2009: (Start) a(n) = 4*a(n-1) - 4*a(n-2) + a(n-3). G.f.: x*(1+9*x+2*x^2)/((1-x)*(x^2-3*x+1)). (End) MATHEMATICA Join[{1}, RecurrenceTable[{a[n] == 3*a[n - 1] - a[n - 2] + 12, a[1] == 13, a[2] == 50}, a, {n, 1, 49}]] (* or *) LinearRecurrence[{4, -4, 1}, {1, 13, 50}, 50] (* G. C. Greubel, Sep 14 2017 *) PROG (PARI) x='x+O('x^50); Vec(x*(1+9*x+2*x^2)/((1-x)*(x^2-3*x+1))) \\ G. C. Greubel, Sep 14 2017 CROSSREFS Cf. A003215, A005891. Sequence in context: A209995 A050410 A121991 * A050491 A022283 A135971 Adjacent sequences:  A121987 A121988 A121989 * A121991 A121992 A121993 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Sep 10 2006 EXTENSIONS Edited and new name based on g.f. by G. C. Greubel and Joerg Arndt, Sep 14 2017 STATUS approved

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Last modified October 21 23:02 EDT 2018. Contains 316431 sequences. (Running on oeis4.)