A004299 Expansion of (1+2*x+x^2)/(1-74*x+x^2).

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

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

Sequence in context: A234176 A116264 A324434 * A049669 A198476 A234778

Adjacent sequences: A004296 A004297 A004298 * A004300 A004301 A004302

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved