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A004293 Expansion of (1+2*x+x^2)/(1-26*x+x^2). 1
1, 28, 728, 18900, 490672, 12738572, 330712200, 8585778628, 222899532128, 5786802056700, 150233953942072, 3900296000437172, 101257462057424400, 2628793717492597228, 68247379192750103528, 1771803065294010094500, 45998632318451512353472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

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..700

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

Index entries for linear recurrences with constant coefficients, signature (26,-1).

FORMULA

From Colin Barker, Apr 16 2016: (Start)

a(n) = sqrt(7/6)*((13+2*sqrt(42))^(-n)*(-1+(13+2*sqrt(42))^(2*n))) for n>0.

a(n) = 26*a(n-1) - a(n-2) for n>2.

(End)

MATHEMATICA

CoefficientList[Series[(1+2*x+x^2)/(1-26*x+x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 13 2012 *)

PROG

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

CROSSREFS

Sequence in context: A239408 A215857 A185987 * A012808 A226991 A277060

Adjacent sequences:  A004290 A004291 A004292 * A004294 A004295 A004296

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified August 20 01:14 EDT 2019. Contains 326136 sequences. (Running on oeis4.)