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A004291 Expansion of (1 + 2*x + x^2)/(1 - 10*x + x^2). 3
1, 12, 120, 1188, 11760, 116412, 1152360, 11407188, 112919520, 1117788012, 11064960600, 109531817988, 1084253219280, 10733000374812, 106245750528840, 1051724504913588, 10410999298607040, 103058268481156812, 1020171685512961080, 10098658586648453988 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified August 18 00:56 EDT 2019. Contains 326059 sequences. (Running on oeis4.)