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A015562 Expansion of x/(1 - 7*x - 5*x^2). 4
0, 1, 7, 54, 413, 3161, 24192, 185149, 1417003, 10844766, 82998377, 635212469, 4861479168, 37206416521, 284752311487, 2179298263014, 16678849398533, 127648437104801, 976933306726272, 7476775332607909, 57222093861886723 (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 (7,5).

FORMULA

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

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Sequence in context: A204258 A081008 A116472 * A243670 A152108 A093742

Adjacent sequences: A015559 A015560 A015561 * A015563 A015564 A015565

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified December 6 10:23 EST 2022. Contains 358630 sequences. (Running on oeis4.)