A356837 Coordination sequence of the {3,5,3} hyperbolic honeycomb.

1, 20, 260, 3212, 39470, 484760, 5953532, 73117640, 897985850, 11028509072, 135445355180, 1663456422080, 20429547136382, 250903113935780, 3081437496506420, 37844317258279532, 464780593592780450, 5708148959489987900, 70103969470537620692, 860973771077827270580

Offset

0,2

Comments

a(n) is the number of cells n steps from an (arbitrarily chosen) central cell in the {3,5,3} honeycomb.

Links

Table of n, a(n) for n=0..19.

Dorota Celińska-Kopczyńska and Eryk Kopczyński, Generating Regular Hyperbolic Honeycombs, arXiv:2208.13816 [cs.CG], 2022.

Formula

Conjectures from Chai Wah Wu, Nov 18 2025: (Start)

a(n) = 13*a(n-1) - 11*a(n-2) + 29*a(n-3) - 29*a(n-4) + 11*a(n-5) - 13*a(n-6) + a(n-7) for n > 7.

G.f.: (x + 1)*(x^6 + 6*x^5 + 5*x^4 + 18*x^3 + 5*x^2 + 6*x + 1)/((x - 1)*(-x^6 + 12*x^5 + x^4 + 30*x^3 + x^2 + 12*x - 1)). (End)

Example

Each icosahedral cell has 20 neighbors, so a(1) = 20.

Crossrefs

Sequence in context: A268764 A081244 A025966 * A041764 A395785 A022111

Adjacent sequences: A356834 A356835 A356836 * A356838 A356839 A356840

Keyword

nonn

Author

Eryk Kopczynski, Aug 31 2022

Status

approved