A015588 Expansion of x/(1 - 10*x - 3*x^2).

0, 1, 10, 103, 1060, 10909, 112270, 1155427, 11891080, 122377081, 1259444050, 12961571743, 133394049580, 1372825211029, 14128434259030, 145402818223387, 1496413485010960, 15400343304779761, 158492673502830490, 1631127764942644183, 16786755669934933300

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (10,3).

Formula

a(n) = 10*a(n-1) + 3*a(n-2).

a(n) = -(1/28)*[5-2*sqrt(7)]^n*sqrt(7) + (1/28)*[5+2*sqrt(7)]^n*sqrt(7), with n>=0. - Paolo P. Lava, Jul 15 2008

Mathematica

Join[{a=0, b=1}, Table[c=10*b+3*a; a=b; b=c, {n, 50}]] (* Vladimir Joseph Stephan Orlovsky, Mar 26 2011 *)
LinearRecurrence[{10, 3}, {0, 1}, 30] (* Vincenzo Librandi, Nov 15 2012 *)

Prog

(Sage) [lucas_number1(n, 10, -3) for n in range(0, 20)] # Zerinvary Lajos, Apr 26 2009
(Magma) [n le 2 select n-1 else 10*Self(n-1) + 3*Self(n-2): n in [1..30]]; // (* Vincenzo Librandi, Nov 15 2012 *)
(PARI) x='x+O('x^30); concat([0], Vec(x/(1-10*x-3*x^2))) \\ G. C. Greubel, Jan 06 2018

Crossrefs

Cf. A000045, A015518.

Sequence in context: A087393 A037596 A037687 * A162667 A227014 A036334

Adjacent sequences: A015585 A015586 A015587 * A015589 A015590 A015591

Keyword

nonn,easy

Author

Olivier Gérard

Status

approved