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

Author

Lewis Chen, Oct 24 2024

Keywords

• nonn
• easy

Comments

Also known as a {4,5} tiling.

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

Links

• 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).

Crossrefs

Cf. A008574, A054888 (dual).

Programs

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

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

Extensions

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