The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A004294 Expansion of (1+2*x+x^2)/(1-34*x+x^2). 1
 1, 36, 1224, 41580, 1412496, 47983284, 1630019160, 55372668156, 1881040698144, 63900011068740, 2170719335639016, 73740557400657804, 2505008232286726320, 85096539340348037076, 2890777329339546534264, 98201332658204234127900, 3335954533049604413814336 (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 Vincenzo Librandi, Table of n, a(n) for n = 0..600 J. M. Alonso, Growth functions of amalgams, in Alperin, ed., Arboreal Group Theory, Springer, pp. 1-34, esp. p. 32. Hacène Belbachir, Soumeya Merwa Tebtoub, László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5. Index entries for linear recurrences with constant coefficients, signature (34,-1). FORMULA From Colin Barker, Apr 16 2016: (Start) a(n) = 3*((17+12*sqrt(2))^(1-n)*(-1+(17+12*sqrt(2))^(2*n)))/(48+34*sqrt(2)) for n>0. a(n) = 34*a(n-1) - a(n-2) for n>2. (End) a(n) = (-(-1)^(2^n) + 3*sqrt(2)*sinh(n*log(17+12*sqrt(2))) + 1)/2. - Ilya Gutkovskiy, Apr 16 2016 MATHEMATICA CoefficientList[Series[(1+2*x+x^2)/(1-34*x+x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Jun 14 2012 *) LinearRecurrence[{34, -1}, {1, 36, 1224}, 20] (* Harvey P. Dale, Mar 29 2019 *) PROG (PARI) Vec((1+2*x+x^2)/(1-34*x+x^2)+O(x^99)) \\ Charles R Greathouse IV, Sep 26 2012 CROSSREFS Pairwise sums of A046176. Sequence in context: A233085 A215858 A103278 * A075760 A113938 A001110 Adjacent sequences:  A004291 A004292 A004293 * A004295 A004296 A004297 KEYWORD nonn,easy AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 1 04:02 EST 2021. Contains 349426 sequences. (Running on oeis4.)