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 A122607 Expansion of x*(8*x^5 + 5*x^4 - x^3 - 5*x^2 - 1)/(x^6 + 3*x^5 + 6*x^4 + 4*x^3 - 5*x^2 + x - 1). 0
 1, 1, 1, 1, 1, 1, 10, 19, -17, -62, 163, 550, -548, -3050, 2665, 19450, -7550, -113534, 8308, 667423, 187462, -3800825, -2366747, 21303154, 21068938, -116488961, -162036530, 621601885, 1153785034, -3216794309, -7799929064, 16026195376, 50784142789, -75764359214, -320876463932 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS Obtained as the top element of the vector resulting from multiplying the n-th power of the 6 X 6 matrix [[0, 1, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 1], [1, 3, 6, 4, -5, 1]] with the column vector which contains only 1's. LINKS Peter Steinbach, Golden fields: a case for the heptagon, Math. Mag. Vol. 70, No. 1, Feb. 1997, 22-31. Index entries for linear recurrences with constant coefficients, signature (1,-5,4,6,3,1). FORMULA G.f.: x*(8*x^5+5*x^4-x^3-5*x^2-1)/(x^6+3*x^5+6*x^4+4*x^3-5*x^2+x-1). - Colin Barker, Nov 08 2012 MATHEMATICA M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {1, 3, 6, 4, -5, 1}}; v[1] = {1, 1, 1, 1, 1, 1}; v[n_] := v[n] = M.v[n - 1] a = Table[Floor[v[n][[1]]], {n, 1, 50}] CROSSREFS Cf. A066170. Sequence in context: A240022 A264386 A173822 * A113703 A103757 A287058 Adjacent sequences:  A122604 A122605 A122606 * A122608 A122609 A122610 KEYWORD sign,easy AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 20 2006 EXTENSIONS Edited by N. J. A. Sloane, Sep 24 2006 Definition changed using Barker's g.f. by Bruno Berselli, Sep 19 2017 STATUS approved

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Last modified October 14 04:37 EDT 2019. Contains 327995 sequences. (Running on oeis4.)