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A015562
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Expansion of x/(1 - 7*x - 5*x^2).
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4
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0, 1, 7, 54, 413, 3161, 24192, 185149, 1417003, 10844766, 82998377, 635212469, 4861479168, 37206416521, 284752311487, 2179298263014, 16678849398533, 127648437104801, 976933306726272, 7476775332607909, 57222093861886723
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OFFSET
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0,3
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (7,5).
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FORMULA
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a(n) = 7*a(n-1) + 5*a(n-2).
a(n) = (1/69)*(7/2 + (1/2)*sqrt(69))^n*sqrt(69) - (1/69)*sqrt(69)*(7/2 - (1/2)*sqrt(69))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008
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MATHEMATICA
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Join[{a=0, b=1}, Table[c=7*b+5*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{7, 5}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
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PROG
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(Sage) [lucas_number1(n, 7, -5) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 7*Self(n-1) + 5*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-7*x-5*x^2))) \\ G. C. Greubel, Dec 30 2017
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CROSSREFS
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Sequence in context: A204258 A081008 A116472 * A243670 A152108 A093742
Adjacent sequences: A015559 A015560 A015561 * A015563 A015564 A015565
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KEYWORD
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nonn,easy
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AUTHOR
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Olivier Gérard
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STATUS
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approved
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