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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 (list; graph; refs; listen; history; text; internal format)
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
AUTHOR
STATUS
approved

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Last modified July 14 02:38 EDT 2024. Contains 374291 sequences. (Running on oeis4.)