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 A102105 a(n) = (19*5^n - 16*3^n + 1) / 4. 1
 1, 12, 83, 486, 2645, 13872, 71303, 362346, 1829225, 9198612, 46150523, 231225006, 1157542205, 5791962552, 28972567343, 144901100466, 724620293585, 3623445841692, 18118262329763, 90594411012726, 452981353155365, 2264934660052032, 11324756983085783 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Sum of the entries in the last row of the 3 X 3 matrix M^n, where M = {{1, 0, 0}, {2, 3, 0}, {3, 4, 5}}. Sum of the entries in the second row of M^n = A048473(n). LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Index entries for linear recurrences with constant coefficients, signature (9,-23,15). FORMULA a(n) = 9*a(n-1) - 23*a(n-2) + 15*a(n-3), a(0)=1,a(1)=12,a(2)=83 (derived from the minimal polynomial of the matrix M). G.f.: (1 + 3*x - 2*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)). - Colin Barker, Mar 03 2017 E.g.f.: (exp(x) - 16*exp(3*x) + 19*exp(5*x))/4. - G. C. Greubel, Oct 27 2019 EXAMPLE a(4) = 2645 = 9*486 - 23*83 + 15*12 = 9*a(3) - 23*a(2) + 15*a(1). a(4) = 2645 since M^4 * {1, 1, 1} = {1, 161, 2645}, where 161 = A048473(4). MAPLE with(linalg): M[1]:=matrix(3, 3, [1, 0, 0, 2, 3, 0, 3, 4, 5]): for n from 2 to 23 do M[n]:=multiply(M[1], M[n-1]) od: 1, seq(multiply(M[n], matrix(3, 1, [1, 1, 1]))[3, 1], n=1..23); seq((19*5^n -16*3^n +1)/4, n=0..30); # G. C. Greubel, Oct 27 2019 MATHEMATICA Table[(19*5^n -16*3^n +1)/4, {n, 0, 30}] (* G. C. Greubel, Oct 27 2019 *) PROG (PARI) Vec((1 + 3*x - 2*x^2) / ((1 - x)*(1 - 3*x)*(1 - 5*x)) + O(x^30)) \\ Colin Barker, Mar 03 2017 (MAGMA) [(19*5^n -16*3^n +1)/4: n in [0..30]]; // G. C. Greubel, Oct 27 2019 (Sage) [(19*5^n -16*3^n +1)/4 for n in (0..30)] # G. C. Greubel, Oct 27 2019 (GAP) List([0..30], n-> (19*5^n -16*3^n +1)/4); # G. C. Greubel, Oct 27 2019 CROSSREFS Cf. A000326, A048473, A094727. Sequence in context: A290715 A175037 A252179 * A275743 A026949 A165127 Adjacent sequences:  A102102 A102103 A102104 * A102106 A102107 A102108 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Dec 30 2004 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 Edited by N. J. A. Sloane, Dec 02 2006 New definition from Ralf Stephan, May 17 2007 STATUS approved

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Last modified December 14 22:42 EST 2019. Contains 329987 sequences. (Running on oeis4.)