A265060 Coordination sequence for (2,4,5) tiling of hyperbolic plane.

1, 3, 5, 8, 12, 16, 21, 28, 36, 46, 60, 77, 98, 126, 162, 207, 265, 340, 435, 557, 714, 914, 1170, 1499, 1920, 2458, 3148, 4032, 5163, 6612, 8468, 10844, 13887, 17785, 22776, 29167, 37353, 47836, 61260, 78452, 100469, 128664, 164772, 211014, 270232, 346069, 443190, 567566, 726846, 930827, 1192053, 1526588

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

Formula

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

Mathematica

CoefficientList[Series[(x + 1)^2 (x^2 + 1) (x^4 + x^3 + x^2 + x + 1)/(x^8 - x^5 - x^4 - 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+1)*(x^4+x^3+x^2+x+1)/(x^8-x^5-x^4-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: A000212 A183139 A094913 * A320849 A255981 A020678

Adjacent sequences: A265057 A265058 A265059 * A265061 A265062 A265063

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 29 2015

Status

approved