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A161007
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a(n+1) = 2*a(n) + 16*a(n-1), a(0)=0, a(1)=1.
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3
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0, 1, 2, 20, 72, 464, 2080, 11584, 56448, 298240, 1499648, 7771136, 39536640, 203411456, 1039409152, 5333401600, 27297349632, 139929124864, 716615843840, 3672097685504, 18810048872448, 96373660712960, 493708103385088, 2529394778177536, 12958119210516480
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OFFSET
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0,3
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COMMENTS
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a(n+1)/a(n) = 1 + Sqrt(17) for large values on n.
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,16).
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FORMULA
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a(n) = ((1+sqrt(17))^n - (1-sqrt(17))^n)/(2*sqrt(17)).
G.f.: -x / (16*x^2+2*x-1). - Colin Barker, Jul 01 2015
a(n) = 2^(n-1)*A006131(n-1). - R. J. Mathar, Mar 08 2021
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MATHEMATICA
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LinearRecurrence[{2, 16}, {0, 1}, 50] (* T. D. Noe, Nov 07 2011 *)
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PROG
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(PARI) concat(0, Vec(-x/(16*x^2+2*x-1) + O(x^40))) \\ Colin Barker, Jul 01 2015
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CROSSREFS
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Sequence in context: A003283 A259110 A135188 * A331760 A098077 A279264
Adjacent sequences: A161004 A161005 A161006 * A161008 A161009 A161010
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KEYWORD
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nonn,easy
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AUTHOR
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Sture Sjöstedt, Jun 02 2009
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STATUS
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approved
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