A004296 Expansion of (1+2*x+x^2)/(1-50*x+x^2).

1, 52, 2600, 129948, 6494800, 324610052, 16224007800, 810875779948, 40527564989600, 2025567373700052, 101237841120013000, 5059866488626949948, 252892086590227484400, 12639544463022747270052, 631724331064547136018200, 31573577008764334053639948

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 (50,-1).

Formula

From Colin Barker, Apr 16 2016: (Start)

a(n) = (sqrt(13/3)*(25+4*sqrt(39))^(-n)*(-1+(25+4*sqrt(39))^(2*n)))/2 for n>0.

a(n) = 50*a(n-1) - a(n-2) for n>2.

(End)

a(n) = (-3*(-1)^(2^n) + 2*sqrt(39)*sinh(n*log(25+4*sqrt(39))) + 3)/6. - Ilya Gutkovskiy, Apr 16 2016

Mathematica

CoefficientList[Series[(1+2*x+x^2)/(1-50*x+x^2), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 25 2012 *)

Prog

(PARI) Vec((1+2*x+x^2)/(1-50*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A342898 A215595 A134552 * A097837 A247628 A370188

Adjacent sequences: A004293 A004294 A004295 * A004297 A004298 A004299

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved