A265058 Coordination sequence for (2,3,8) tiling of hyperbolic plane.

1, 3, 5, 7, 9, 12, 16, 21, 27, 33, 40, 49, 61, 76, 94, 116, 142, 174, 214, 264, 326, 401, 493, 606, 745, 917, 1129, 1390, 1710, 2103, 2587, 3183, 3917, 4820, 5931, 7297, 8977, 11045, 13590, 16722, 20575, 25315, 31147, 38322, 47151, 58015, 71382, 87828, 108062, 132958, 163590, 201280, 247654

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

J. W. Cannon, P. Wagreich, Growth functions of surface groups, Mathematische Annalen, 1992, Volume 293, pp. 239-257. See Prop. 3.1.

Index entries for linear recurrences with constant coefficients, signature (0, 0, 1, 0, 1, 0, 1, 0, 0, -1).

Formula

G.f.: (x+1)^2*(x^2+x+1)*(x^6+x^4+x^2+1)/(x^10-x^7-x^5-x^3+1).

Mathematica

CoefficientList[Series[(x + 1)^2 (x^2 + x + 1) (x^6 + x^4 + x^2 + 1)/(x^10 - x^7 - x^5 - x^3 + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)

Prog

(PARI) x='x+O('x^50); Vec((x+1)^2*(x^2+x+1)*(x^6+x^4+x^2+1)/(x^10-x^7-x^5-x^3+1)) \\ G. C. Greubel, Aug 06 2017

Crossrefs

Coordination sequences for triangular tilings of hyperbolic space: A001630, A007283, A054886, A078042, A096231, A163876, A179070, A265057, A265058, A265059, A265060, A265061, A265062, A265063, A265064, A265065, A265066, A265067, A265068, A265069, A265070, A265071, A265072, A265073, A265074, A265075, A265076, A265077.

Sequence in context: A265057 A122643 A194240 * A265059 A349828 A096231

Adjacent sequences: A265055 A265056 A265057 * A265059 A265060 A265061

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 29 2015

Status

approved