A004297 Expansion of (1+2*x+x^2)/(1-58*x+x^2).

1, 60, 3480, 201780, 11699760, 678384300, 39334589640, 2280727814820, 132242878669920, 7667806235040540, 444600518753681400, 25779162281478480660, 1494746811806998196880, 86669535922524416938380, 5025338336694609184229160, 291382953992364808268352900

Offset

0,2

References

P. de la Harpe, Topics in Geometric Group Theory, Univ. Chicago Press, 2000, p. 160, middle display.

Links

Harvey P. Dale, 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 (58, -1).

Formula

a(0)=1, a(1)=60, a(2)=3480, a(n) = 58*a(n-1)-a(n-2). - Harvey P. Dale, Dec 30 2011

From Colin Barker, Apr 16 2016: (Start)

a(n) = sqrt(15/14)*((29+2*sqrt(210))^(-n)*(-1+(29+2*sqrt(210))^(2*n))) for n>0.

a(n) = 58*a(n-1) - a(n-2) for n>2.

(End)

a(n) = -(-1)^(2^n)/2 + sqrt(30/7)*sinh(n*log(29+2*sqrt(210))) + 1/2. - Ilya Gutkovskiy, Apr 16 2016

Mathematica

CoefficientList[Series[(1+2x+x^2)/(1-58x+x^2), {x, 0, 30}], x] (* or *) Join[{1}, LinearRecurrence[{58, -1}, {60, 3480}, 30]] (* Harvey P. Dale, Dec 30 2011 *)

Prog

(PARI) Vec((1+2*x+x^2)/(1-58*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012

Crossrefs

Sequence in context: A230568 A180373 A264947 * A223657 A264369 A053401

Adjacent sequences: A004294 A004295 A004296 * A004298 A004299 A004300

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved