A265072 Coordination sequence for (3,3,5) tiling of hyperbolic plane.

1, 3, 6, 10, 16, 25, 38, 57, 86, 130, 196, 295, 444, 669, 1008, 1518, 2286, 3443, 5186, 7811, 11764, 17718, 26686, 40193, 60536, 91175, 137322, 206826, 311508, 469173, 706638, 1064293, 1602970, 2414290, 3636248, 5476683, 8248628, 12423553, 18711556, 28182142, 42446130, 63929631, 96286698, 145020831, 218421048

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 (1,0,1,0,1,-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^2 + x + 1) (x^4 + x^3 + x^2 + x + 1)/(x^6 - x^5 - x^3 - x + 1), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 30 2015 *)
LinearRecurrence[{1,0,1,0,1,-1},{1,3,6,10,16,25,38},50] (* Harvey P. Dale, Oct 07 2022 *)

PARI

x='x+O('x^50); Vec((x^2+x+1)*(x^4+x^3+x^2+x+1)/(x^6-x^5-x^3-x+1)) \\ G. C. Greubel, Aug 07 2017

Formula

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