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..500
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 (50,-1).
FORMULA
From Colin Barker, Apr 16 2016: (Start)
a(n) = (sqrt(13/3)*(25+4*sqrt(39))^(-n)*(-1+(25+4*sqrt(39))^(2*n)))/2 for n>0.
a(n) = 50*a(n-1) - a(n-2) for n>2.
(End)
a(n) = (-3*(-1)^(2^n) + 2*sqrt(39)*sinh(n*log(25+4*sqrt(39))) + 3)/6. - Ilya Gutkovskiy, Apr 16 2016
MATHEMATICA
CoefficientList[Series[(1+2*x+x^2)/(1-50*x+x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2012 *)
PROG
(PARI) Vec((1+2*x+x^2)/(1-50*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved