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 A122006 Expansion of x^2*(1-x)/((1-3*x)*(1-3*x^2)). 3
 0, 1, 2, 9, 24, 81, 234, 729, 2160, 6561, 19602, 59049, 176904, 531441, 1593594, 4782969, 14346720, 43046721, 129133602, 387420489, 1162241784, 3486784401, 10460294154, 31381059609, 94143001680, 282429536481, 847288078002, 2541865828329, 7625595890664 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS Limit(n->infinity) a(n+1)/a(n)=3. The sequence can be created by multiplying the n-th power of the matrix [[0,1,2],[1,2,0],[2,0,1]], multiplying from the right with the vector [1,0,0] and taking the middle element of the resulting vector. REFERENCES Alain M. Robert, "Linear Algebra, Examples and Applications", World Scientific, 2005, p. 58. LINKS Colin Barker, Table of n, a(n) for n = 1..1000 Index entries for linear recurrences with constant coefficients, signature (3,3,-9). FORMULA a(n) = 3*a(n-1) + 3*a(n-2) - 9*a(n-3). - Philippe Deléham, Mar 09 2009 From Colin Barker, Sep 23 2016: (Start) a(n) = 3^(n-2) for n even. a(n) = 3^(n-2)-3^((n-3)/2) for n odd. (End) MATHEMATICA M = {{0, 1, 2}, {1, 2, 0}, {2, 0, 1}} v[1] = {1, 0, 0} v[n_] := v[n] = M.v[n - 1] a1 = Table[v[n][[2]], {n, 1, 50}] PROG (PARI) concat(0, Vec(x^2*(1-x)/((1-3*x)*(1-3*x^2)) + O(x^40))) \\ Colin Barker, Sep 23 2016 CROSSREFS Cf. A007179. Sequence in context: A248436 A354016 A222667 * A200086 A143561 A027302 Adjacent sequences:  A122003 A122004 A122005 * A122007 A122008 A122009 KEYWORD nonn,easy AUTHOR Roger L. Bagula and Gary W. Adamson, Sep 11 2006 STATUS approved

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Last modified June 25 03:59 EDT 2022. Contains 354835 sequences. (Running on oeis4.)