A004291 Expansion of (1 + 2*x + x^2)/(1 - 10*x + x^2).

1, 12, 120, 1188, 11760, 116412, 1152360, 11407188, 112919520, 1117788012, 11064960600, 109531817988, 1084253219280, 10733000374812, 106245750528840, 1051724504913588, 10410999298607040, 103058268481156812, 1020171685512961080, 10098658586648453988

Offset

0,2

References

J. M. Alonso, Growth functions of amalgams, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.

Links

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

Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.

Index entries for linear recurrences with constant coefficients, signature (10,-1).

Formula

a(n) = 12*A004189(n), n> 0. - R. J. Mathar, Oct 29 2012

a(n) = sqrt(3/2)*(-(5 - 2*sqrt(6))^n + (5 + 2*sqrt(6))^n) for n > 0. - Colin Barker, Jan 25 2016

For n > 0: a(n) = 10*a(n-1) - a(n-2) with a(0) = 0, a(1) = 12. - A.H.M. Smeets, Jul 25 2017

Mathematica

CoefficientList[Series[(1+2*x+x^2)/(1-10*x+x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Jun 13 2012 *)

Prog

(PARI) Vec((1+2*x+x^2)/(1-10*x+x^2) + O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Pairwise sums of A054320.

Sequence in context: A129329 A266393 A129332 * A001754 A037511 A037694

Adjacent sequences: A004288 A004289 A004290 * A004292 A004293 A004294

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved