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A015611 a(n) = 12*a(n-1) + 7*a(n-2). 3
0, 1, 12, 151, 1896, 23809, 298980, 3754423, 47145936, 592032193, 7434407868, 93357119767, 1172326292280, 14721415345729, 184863268194708, 2321409125756599, 29150952386442144, 366061292517601921, 4596792176916318060, 57723935170619030167 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..900

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

FORMULA

a(n) = (1/86)*sqrt(43)*((6+sqrt(43))^n - (6-sqrt(43))^n). - Paolo P. Lava, Jan 13 2009

G.f.: x/(1 - 12*x - 7*x^2). - Vincenzo Librandi, Nov 22 2012

MATHEMATICA

Join[{a=0, b=1}, Table[c=12*b+7*a; a=b; b=c, {n, 60}]] (* Vladimir Joseph Stephan Orlovsky, Jan 31 2011 *)

CoefficientList[Series[x/(1 - 12x - 7x^2), {x, 0, 30}], x] (* or *) LinearRecurrence[{12, 7}, {0, 1}, 30] (* Vincenzo Librandi, Nov 22 2012 *)

PROG

(Sage) [lucas_number1(n, 12, -7) for n in range(0, 18)] # Zerinvary Lajos, Apr 29 2009

(Magma) [n le 2 select n-1 else 12*Self(n-1) + 7*Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 22 2012

(PARI) x='x+O('x^30); concat([0], Vec(x/(1-12*x-7*x^2))) \\ G. C. Greubel, Dec 30 2017

CROSSREFS

Sequence in context: A060917 A113358 A293153 * A127650 A286432 A189548

Adjacent sequences: A015608 A015609 A015610 * A015612 A015613 A015614

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

STATUS

approved

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Last modified November 29 18:13 EST 2022. Contains 358431 sequences. (Running on oeis4.)