A265061 Coordination sequence for (2,4,6) tiling of hyperbolic plane.

1, 3, 5, 8, 12, 17, 24, 33, 45, 61, 83, 114, 155, 210, 286, 389, 529, 720, 979, 1331, 1810, 2462, 3349, 4554, 6193, 8423, 11455, 15579, 21188, 28815, 39188, 53296, 72483, 98577, 134064, 182327, 247965, 337232, 458636, 623745, 848292, 1153677, 1569001, 2133841, 2902023, 3946750, 5367579, 7299906, 9927870, 13501901

Offset: 0

Author

N. J. A. Sloane, Dec 29 2015

Keywords

• nonn
• easy

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 (1, -1, 2, -1, 2, -1, 1, -1).

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.

Programs

Mathematica

CoefficientList[Series[(x + 1)^2 (x^2 + 1) (x^4 + x^2 + 1)/(x^8 - x^7 + x^6 - 2 x^5 + x^4 - 2 x^3 + x^2 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)

PARI

Vec((x+1)^2*(x^2+1)*(x^4+x^2+1)/(x^8-x^7+x^6-2*x^5+x^4-2*x^3+x^2-x+1) + O(x^100)) \\ Altug Alkan, Dec 29 2015

Formula

G.f.: (x+1)^2*(x^2+1)*(x^4+x^2+1)/(x^8-x^7+x^6-2*x^5+x^4-2*x^3+x^2-x+1).