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A015548 Expansion of x/(1 - 5*x - 12*x^2). 5
0, 1, 5, 37, 245, 1669, 11285, 76453, 517685, 3505861, 23741525, 160777957, 1088788085, 7373275909, 49931836565, 338138493733, 2289874507445, 15507034462021, 105013666399445, 711152745541477, 4815927724500725, 32613471569001349 (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 (5,12).

FORMULA

a(n) = 2*A099919(n-1) + 1, for n>=1.

a(n) = 5 a(n-1) + 12 a(n-2).

a(n) = (1/73)*(5/2 + (1/2)*sqrt(73))^n*sqrt(73) - (1/73)*(5/2 - (1/2)*sqrt(73))^n*sqrt(73), with n >= 0. - Paolo P. Lava, Aug 06 2008

MATHEMATICA

Join[{a=0, b=1}, Table[c=5*b+12*a; a=b; b=c, {n, 100}]] (* Vladimir Joseph Stephan Orlovsky, Jan 16 2011 *)

LinearRecurrence[{5, 12}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)

PROG

(Sage) [lucas_number1(n, 5, -12) for n in xrange(0, 21)] # Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 5*Self(n-1) + 12*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 13 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-5*x-12*x^2))) \\ G. C. Greubel, Jan 16 2018

CROSSREFS

Sequence in context: A088582 A088583 A202556 * A183385 A054417 A080507

Adjacent sequences:  A015545 A015546 A015547 * A015549 A015550 A015551

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 12 14:35 EST 2019. Contains 329058 sequences. (Running on oeis4.)