A265066 Coordination sequence for (2,5,7) tiling of hyperbolic plane.

1, 3, 5, 8, 13, 20, 30, 45, 67, 100, 149, 221, 329, 491, 731, 1087, 1618, 2409, 3586, 5338, 7946, 11828, 17607, 26209, 39013, 58074, 86448, 128683, 191552, 285138, 424447, 631817, 940501, 1399997, 2083987, 3102151, 4617754, 6873828, 10232143, 15231214, 22672656, 33749729, 50238677, 74783553, 111320204, 165707396

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 (-1, 0, 1, 2, 3, 3, 3, 2, 1, 0, -1, -1).

Formula

G.f.: (x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(x+1)^2/(x^12+x^11-x^9-2*x^8-3*x^7-3*x^6-3*x^5-2*x^4-x^3+x+1).

Mathematica

CoefficientList[Series[(x^6 + x^5 + x^4 + x^3 + x^2 + x + 1) (x^4 + x^3 + x^2 + x + 1) (x + 1)^2 / (x^12 + x^11 - x^9 - 2 x^8 - 3 x^7 - 3 x^6 - 3 x^5 - 2 x^4 - x^3 + x + 1), {x, 0, 45}], x] (* Vincenzo Librandi, Jan 20 2016 *)

Prog

(PARI) Vec((x^6+x^5+x^4+x^3+x^2+x+1)*(x^4+x^3+x^2+x+1)*(x+1)^2/(x^12+x^11-x^9-2*x^8-3*x^7-3*x^6-3*x^5-2*x^4-x^3+x+1) + O(x^50)) \\ Michel Marcus, Jan 20 2016

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: A245934 A099351 A265065 * A265067 A265068 A227547

Adjacent sequences: A265063 A265064 A265065 * A265067 A265068 A265069

Keyword

nonn

Author

N. J. A. Sloane, Dec 29 2015

Status

approved