A377322 Number of cells that are a distance of n away in an order-5 hyperbolic square tiling.

1, 4, 12, 28, 64, 148, 340, 780, 1792, 4116, 9452, 21708, 49856, 114500, 262964, 603932, 1387008, 3185444, 7315788, 16801660, 38587200, 88620532, 203528596, 467429932, 1073513728, 2465464116, 5662259500, 13004116524, 29865647552, 68590349988, 157526673524

Offset

0,2

Comments

Also known as a {4,5} tiling.

The formula given in the MathOverflow answer (4 * A033303) is erroneous after n=3.

Links

Table of n, a(n) for n=0..30.

M. Lavrov, Description of the order-5 square tiling of the hyperbolic plane as a graph, MathOverflow

EC Puzzle Hunt, Solution: Tower Navigation

Index entries for coordination sequences.

Index entries for linear recurrences with constant coefficients, signature (2,0,2,-1).

Formula

G.f.: (1 + 2*x + 4*x^2 + 2*x^3 + x^4)/(1 - 2*x - 2*x^3 + x^4). - Andrew Howroyd, Feb 12 2025

Prog

(PARI) Vec((1 + 2*x + 4*x^2 + 2*x^3 + x^4)/(1 - 2*x - 2*x^3 + x^4) + O(x^31)) \\ Andrew Howroyd, Feb 12 2025

Crossrefs

Cf. A008574, A054888 (dual).

Sequence in context: A339124 A317233 A309917 * A034508 A173380 A002932

Adjacent sequences: A377319 A377320 A377321 * A377323 A377324 A377325

Keyword

nonn,easy

Author

Lewis Chen, Oct 24 2024

Extensions

a(20) onwards from Andrew Howroyd, Feb 12 2025

Status

approved