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Coordination sequence of the {4,3,5} hyperbolic honeycomb.
1

%I #20 Nov 06 2022 08:52:51

%S 1,6,30,126,498,1982,7854,31014,122562,484422,1914254,7564542,

%T 29893554,118131966,466827678,1844789414,7290156162,28808903814,

%U 113845717662,449890341534,1777856189330,7025651266782,27763649373966,109715127592326,433567254075330,1713351367231142,6770744053574286

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

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

%H Dorota Celińska-Kopczyńska and Eryk Kopczyński, <a href="https://arxiv.org/abs/2208.13816">Generating Regular Hyperbolic Honeycombs</a>, arXiv:2208.13816 [cs.CG], 2022.

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

%e For example, each cell has 6 neighbors, so a(1) = 6.

%e Each of these has 6 neighbors -- 5 not counting the original cube -- so a(2)=30.

%Y First differences of A247308.

%K nonn

%O 0,2

%A _Eryk Kopczynski_, Aug 31 2022