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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
OFFSET
0,2
REFERENCES
P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.
LINKS
J. M. Alonso, Growth functions of amalgams, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32.
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
KEYWORD
nonn,easy
STATUS
approved