A265063 Coordination sequence for (2,4,8) tiling of hyperbolic plane.

1, 3, 5, 8, 12, 17, 25, 37, 53, 75, 107, 152, 216, 309, 441, 628, 895, 1275, 1816, 2588, 3689, 5257, 7491, 10675, 15211, 21675, 30888, 44016, 62723, 89381, 127368, 181499, 258637, 368560, 525200, 748413, 1066493, 1519757, 2165661, 3086079, 4397679, 6266716, 8930104, 12725445, 18133825, 25840796, 36823271, 52473355

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

Formula

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

Mathematica

CoefficientList[Series[(x^2 + 1)*(x^4 + 1)*(x + 1)^2/(x^8 - x^7 - x^5 + x^4 - x^3 - x + 1), {x, 0, 50}], x] (* G. C. Greubel, Aug 07 2017 *)
LinearRecurrence[{1, 0, 1, -1, 1, 0, 1, -1}, {1, 3, 5, 8, 12, 17, 25, 37, 53}, 50] (* Harvey P. Dale, Jul 26 2024 *)

Prog

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

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: A167385 A265061 A265062 * A098202 A164653 A001973

Adjacent sequences: A265060 A265061 A265062 * A265064 A265065 A265066

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 29 2015

Status

approved