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 (74,-1).
FORMULA
From Colin Barker, Apr 16 2016: (Start)
a(n) = (37+6*sqrt(38))^(1-n)*(-228+37*sqrt(38))*(-1+(37+6*sqrt(38))^(2*n))/6 for n>0.
a(n) = 74*a(n-1) - a(n-2) for n>2.
(End)
a(n) = (-3*(-1)^(2^n) + 2*sqrt(38)*sinh(n*log(37+6*sqrt(38))) + 3)/6. - Ilya Gutkovskiy, Apr 16 2016
MATHEMATICA
CoefficientList[Series[(1+2*x+x^2)/(1-74*x+x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 14 2012 *)
LinearRecurrence[{74, -1}, {1, 76, 5624}, 20] (* Harvey P. Dale, Jan 05 2020 *)
PROG
(PARI) Vec((1+2*x+x^2)/(1-74*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved