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A004295
Expansion of (1+2*x+x^2)/(1-42*x+x^2).
1
1, 44, 1848, 77572, 3256176, 136681820, 5737380264, 240833289268, 10109260768992, 424348119008396, 17812511737583640, 747701144859504484, 31385635572361604688, 1317448992894327892412, 55301472065989409876616, 2321344377778660886925460
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(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
Sequence in context: A231262 A223049 A278793 * A162882 A163230 A163748
KEYWORD
nonn,easy
STATUS
approved