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..600
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 (42,-1).
FORMULA
From Colin Barker, Apr 16 2016: (Start)
a(n) = sqrt(11/10)*((21+2*sqrt(110))^(-n)*(-1+(21+2*sqrt(110))^(2*n))) for n>0.
a(n) = 42*a(n-1) - a(n-2) for n>2.
(End)
a(n) = -(-1)^(2^n)/2 + sqrt(22/5)*sinh(n*log(21+2*sqrt(110))) + 1/2. - Ilya Gutkovskiy, Apr 16 2016
MATHEMATICA
CoefficientList[Series[(1+2*x+x^2)/(1-42*x+x^2), {x, 0, 50}], x] (* Vincenzo Librandi, Feb 25 2012 *)
LinearRecurrence[{42, -1}, {1, 44, 1848}, 20] (* Harvey P. Dale, Oct 21 2024 *)
PROG
(PARI) Vec((1+2*x+x^2)/(1-42*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved