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