OFFSET
1,3
COMMENTS
A stereographic projection of the {5,oo} tiling on the Poincaré disk can be obtained via the Christensson link.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..1000
Malin Christensson, Make hyperbolic tilings of images, web page, 2019.
FORMULA
For n even, a(n) = C(2n,n/2)/(3n/2+1).
For n odd, a(n) = 4*C(2n-1,(n-1)/2)/(3n+1).
a(n+2)/a(n) ~ 256/27. a(2m+1)/a(2m) ~ 32/9; a(2m)/a(2m-1) ~ 8/3.
G.f.: G(z^2)+z*G(z^2)^2, where G(z)=1+z*G(z)^4, the generating function for A002293.
a(2m) = A002293(m) ~ (4^4/3^3)^m*sqrt(4/(2*Pi*(3*m)^3)). - Robert A. Russell, Jul 15 2024
MATHEMATICA
p=5; Table[If[EvenQ[n], Binomial[(p-1)n/2, n/2]/((p-2)n/2+1), If[OddQ[p], (p-1)Binomial[(p-1)n/2-1, (n-1)/2]/((p-2)n+1), p Binomial[(p-1)n/2-1/2, (n-1)/2]/((p-2)n+2)]], {n, 35}]
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Robert A. Russell, Jan 23 2024
STATUS
approved