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A015572 Expansion of x/(1 - 7*x - 12*x^2). 1
0, 1, 7, 61, 511, 4309, 36295, 305773, 2575951, 21700933, 182817943, 1540136797, 12974772895, 109305051829, 920832637543, 7757489084749, 65352415243759, 550556775723301, 4638126412988215, 39073566199597117, 329172480353038399, 2773090156866434197, 23361700862301500167 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (7,12).

FORMULA

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A218228 A155599 A104093 * A066443 A108448 A218473

Adjacent sequences:  A015569 A015570 A015571 * A015573 A015574 A015575

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified April 12 00:18 EDT 2021. Contains 342911 sequences. (Running on oeis4.)