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A015566
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Expansion of x/(1 - 7*x - 9*x^2).
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3
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0, 1, 7, 58, 469, 3805, 30856, 250237, 2029363, 16457674, 133467985, 1082394961, 8777976592, 71187390793, 577313524879, 4681881191290, 37968990062941, 307919861162197, 2497159938701848, 20251398321372709, 164234227697925595
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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 (7,9).
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FORMULA
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a(n) = 7*a(n-1) + 9*a(n-2).
a(n) = -(1/85)*(7/2 - (1/2)*sqrt(85))^n*sqrt(85) + (1/85)*sqrt(85)*(7/2 + (1/2)*sqrt(85))^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+9*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 17 2011 *)
LinearRecurrence[{7, 9}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)
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PROG
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(Sage) [lucas_number1(n, 7, -9) for n in range(0, 20)] # Zerinvary Lajos, Apr 24 2009
(MAGMA) [n le 2 select n-1 else 7*Self(n-1) + 9*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-9*x^2))) \\ G. C. Greubel, Dec 31 2017
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CROSSREFS
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Sequence in context: A266051 A202975 A051816 * A238810 A334610 A244469
Adjacent sequences: A015563 A015564 A015565 * A015567 A015568 A015569
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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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