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A015578 Expansion of x/(1 - 8*x - 11*x^2). 1
0, 1, 8, 75, 688, 6329, 58200, 535219, 4921952, 45263025, 416245672, 3827858651, 35201571600, 323719017961, 2976969431288, 27376664647875, 251759980927168, 2315223158543969, 21291145058550600, 195796615212388459, 1800575517343164272, 16558366906081587225, 152273265939427504792 (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 (8,11).

FORMULA

a(n) = 8*a(n-1) + 11*a(n-2).

a(n) = -(1/18)*sqrt(3)*(4-3*sqrt(3))^n + (1/18)*sqrt(3)*(4+3*sqrt(3))^n, with n >= 0. - Paolo P. Lava, Jun 25 2008

MATHEMATICA

Transpose[NestList[{Last[#], 8Last[#]+11First[#]}&, {0, 1}, 20]] [[1]]  (* Harvey P. Dale, Mar 14 2011 *)

LinearRecurrence[{8, 11}, {0, 1}, 30] (* Vincenzo Librandi, Nov 14 2012 *)

PROG

(Sage) [lucas_number1(n, 8, -11) for n in range(0, 19)] # Zerinvary Lajos, Apr 25 2009

(MAGMA) [n le 2 select n-1 else 8*Self(n-1) + 11*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 14 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-8*x-11*x^2))) \\ G. C. Greubel, Jan 06 2018

CROSSREFS

Sequence in context: A123661 A288487 A123003 * A145600 A268085 A231617

Adjacent sequences:  A015575 A015576 A015577 * A015579 A015580 A015581

KEYWORD

nonn,easy,changed

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 15 04:23 EST 2019. Contains 329991 sequences. (Running on oeis4.)