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A004299
Expansion of (1+2*x+x^2)/(1-74*x+x^2).
1
1, 76, 5624, 416100, 30785776, 2277731324, 168521332200, 12468300851476, 922485741677024, 68251476583248300, 5049686781418697176, 373608570348400342724, 27641984519000206664400, 2045133245835666892822876, 151312218207320349862228424
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) = (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
Sequence in context: A234176 A116264 A324434 * A049669 A198476 A234778
KEYWORD
nonn,easy
STATUS
approved