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A015544 Lucas sequence U(5,-8): a(n+1) = 5*a(n) + 8*a(n-1), a(0)=0, a(1)=1. 3
0, 1, 5, 33, 205, 1289, 8085, 50737, 318365, 1997721, 12535525, 78659393, 493581165, 3097180969, 19434554165, 121950218577, 765227526205, 4801739379641, 30130517107845, 189066500576353, 1186376639744525, 7444415203333449, 46713089134623445 (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 (5,8).

FORMULA

a(n) = 5*a(n-1) + 8*a(n-2).

a(n) = (1/57)*sqrt(57)*[5/2 + (1/2)*sqrt(57)]^n - (1/57)*sqrt(57)*[5/2 - (1/2)*sqrt(57)]^n, with n>=0. - Paolo P. Lava, Aug 05 2008

G.f.: x/(1 - 5*x - 8*x^2). - M. F. Hasler, Mar 06 2009

MATHEMATICA

a[n_]:=(MatrixPower[{{1, 2}, {1, -6}}, n].{{1}, {1}})[[2, 1]]; Table[Abs[a[n]], {n, -1, 40}] (* Vladimir Joseph Stephan Orlovsky, Feb 19 2010 *)

LinearRecurrence[{5, 8}, {0, 1}, 30] (* Vincenzo Librandi, Nov 13 2012 *)

PROG

(PARI) A015544(n)=imag((2+quadgen(57))^n) \\ M. F. Hasler, Mar 06 2009

(Sage) [lucas_number1(n, 5, -8) for n in range(0, 21)] # Zerinvary Lajos, Apr 24 2009

(MAGMA) [n le 2 select n-1 else 5*Self(n-1) + 8*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 - 8*x^2))) \\ G. C. Greubel, Jan 01 2018

CROSSREFS

Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015441, A015443, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226.

Sequence in context: A091056 A244901 A197675 * A155597 A250163 A164538

Adjacent sequences:  A015541 A015542 A015543 * A015545 A015546 A015547

KEYWORD

nonn,easy

AUTHOR

Olivier Gérard

EXTENSIONS

More precise definition by M. F. Hasler, Mar 06 2009

STATUS

approved

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Last modified December 4 02:40 EST 2021. Contains 349469 sequences. (Running on oeis4.)