A265064 Coordination sequence for (2,5,5) tiling of hyperbolic plane.

1, 3, 5, 8, 13, 19, 26, 37, 53, 74, 103, 145, 204, 285, 399, 560, 785, 1099, 1540, 2159, 3025, 4238, 5939, 8323, 11662, 16341, 22899, 32088, 44963, 63005, 88288, 123715, 173357, 242920, 340397, 476987, 668386, 936589, 1312413, 1839042, 2576991, 3611057, 5060060, 7090501, 9935695, 13922576, 19509265, 27337715

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 (0, 1, 1, 1, 0, -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^4 + x^3 + x^2 + x + 1) (x + 1)^2 / (x^6 - x^4 - x^3 - x^2 + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)
LinearRecurrence[{0,1,1,1,0,-1},{1,3,5,8,13,19,26},50] (* Harvey P. Dale, Mar 29 2025 *)

PARI

Vec((x^4+x^3+x^2+x+1)*(x+1)^2/(x^6-x^4-x^3-x^2+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

Formula

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