A356835 Coordination sequence of the {4,3,5} hyperbolic honeycomb.

1, 6, 30, 126, 498, 1982, 7854, 31014, 122562, 484422, 1914254, 7564542, 29893554, 118131966, 466827678, 1844789414, 7290156162, 28808903814, 113845717662, 449890341534, 1777856189330, 7025651266782, 27763649373966, 109715127592326, 433567254075330, 1713351367231142, 6770744053574286

Offset

0,2

Comments

a(n) is the number of cells n steps from an (arbitrarily chosen) central cell in the {4,3,5} honeycomb.

Links

Table of n, a(n) for n=0..26.

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

Formula

a(n) = A247308(n) - A247308(n-1).

Example

For example, each cell has 6 neighbors, so a(1) = 6.
Each of these has 6 neighbors -- 5 not counting the original cube -- so a(2)=30.

Crossrefs

First differences of A247308.

Sequence in context: A074009 A248328 A366058 * A344344 A002446 A002934

Adjacent sequences: A356832 A356833 A356834 * A356836 A356837 A356838

Keyword

nonn

Author

Eryk Kopczynski, Aug 31 2022

Status

approved