A265059 Coordination sequence for (2,3,9) tiling of hyperbolic plane.

1, 3, 5, 7, 9, 12, 16, 21, 28, 36, 45, 56, 70, 89, 113, 143, 181, 228, 287, 361, 455, 575, 726, 916, 1155, 1456, 1836, 2315, 2920, 3684, 4647, 5861, 7391, 9321, 11756, 14827, 18701, 23587, 29749, 37520, 47320, 59681, 75272, 94936, 119737, 151016, 190466, 240221, 302973, 382119, 481941, 607840, 766627

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, 1, 0, 0, 1, 0, 0, 1, 0, -1).

Formula

G.f.: (x+1)^2*(x^2+x+1)*(x^6+x^3+1)/(x^10-x^8-x^5-x^2+1).

Mathematica

CoefficientList[Series[(x + 1)^2 (x^2 + x + 1) (x^6 + x^3 + 1)/(x^10 - x^8 - x^5 - x^2 + 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^3+1)/(x^10-x^8-x^5-x^2+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: A122643 A194240 A265058 * A349828 A096231 A362133

Adjacent sequences: A265056 A265057 A265058 * A265060 A265061 A265062

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 29 2015

Status

approved