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A015572
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Expansion of x/(1 - 7*x - 12*x^2).
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1
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0, 1, 7, 61, 511, 4309, 36295, 305773, 2575951, 21700933, 182817943, 1540136797, 12974772895, 109305051829, 920832637543, 7757489084749, 65352415243759, 550556775723301, 4638126412988215, 39073566199597117, 329172480353038399, 2773090156866434197, 23361700862301500167
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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 (7,12).
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FORMULA
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a(n) = 7*a(n-1) + 12*a(n-2).
a(n) = (1/97)*sqrt(97)*(7/2 + (1/2)*sqrt(97))^n - (1/97)*sqrt(97)*(7/2 - (1/2)*sqrt(97))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008
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MATHEMATICA
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a[n_]:=(MatrixPower[{{1, 4}, {1, -8}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)
CoefficientList[Series[x/(1-7x-12x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{7, 12}, {0, 1}, 30] (* Harvey P. Dale, Jan 11 2012 *)
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PROG
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(Sage) [lucas_number1(n, 7, -12) for n in range(0, 20)] # Zerinvary Lajos, Apr 24 2009
(Magma) [n le 2 select n-1 else 7*Self(n-1) + 12*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-12*x^2))) \\ G. C. Greubel, Jan 06 2018
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CROSSREFS
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Sequence in context: A218228 A155599 A104093 * A066443 A108448 A218473
Adjacent sequences: A015569 A015570 A015571 * A015573 A015574 A015575
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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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