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 A095898 The (1,1)-term of the 3 X 3 matrix M^n, where M = [1,2,3 / 4,7,11 / 6,10,16]. 1
 1, 27, 649, 15603, 375121, 9018507, 216819289, 5212681443, 125321173921, 3012920855547, 72435421707049, 1741463041824723, 41867548425500401, 1006562625253834347, 24199370554517524729, 581791455933674427843, 13987194312962703792961, 336274454967038565458907 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 LINKS Colin Barker, Table of n, a(n) for n = 1..700 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (24,1). FORMULA a(n) = 24*a(n-1) + a(n-2) for n>=3; a(1)=1, a(2)=27 (follows from the minimal polynomial of the matrix M). G.f.: (x+3*x^2) / (1-24*x-x^2). - Philippe Deléham, Nov 21 2008 a(n) = (-12 - sqrt(145))^(-n)*(87+7*sqrt(145) + (-289-24*sqrt(145))^n*(87-7*sqrt(145))) / 58. - Colin Barker, Mar 02 2017 EXAMPLE a(4)=15603 because M^4 = [15603,26590,42193 / 56642,96527,153169 / 82078,139874,221952]. Alternatively, a(4) = 24*649+27 = 15603. MAPLE a[1]:=1: a[2]:=27: for n from 3 to 18 do a[n]:=24*a[n-1]+a[n-2] od: seq(a[n], n=1..18); PROG (PARI) Vec(x*(1 + 3*x) / (1 - 24*x - x^2) + O(x^30)) \\ Colin Barker, Mar 02 2017 CROSSREFS Cf. A083412, A035513, A003622, A001950, A000201. Sequence in context: A060603 A116988 A113364 * A014914 A157461 A162827 Adjacent sequences:  A095895 A095896 A095897 * A095899 A095900 A095901 KEYWORD nonn,easy AUTHOR Gary W. Adamson, Jun 12 2004 EXTENSIONS Corrected by T. D. Noe, Nov 07 2006 Edited by N. J. A. Sloane, Dec 16 2006 STATUS approved

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Last modified October 19 11:09 EDT 2019. Contains 328216 sequences. (Running on oeis4.)