4,1

A stereographic projection of the {6,oo} tiling on the Poincaré disk can be obtained via the Christersson link. Each member of a chiral pair is a reflection but not a rotation of the other.

Malin Christersson, Make hyperbolic tilings of images, web page, 2019.

a(n) = A221184(n-1) - A004127(n) = (A221184(n-1) - A143546(n)) / 2 = A004127(n) - A143546(n).

G.f.: (5*G(z) - 2*G(z)^2 - 3*G(z^2) - 5*z*G(z^2)^3 + 2*z*G(z^3)^2 + 2*z*G(z^6)) / 12, where G(z)=1+z*G(z)^5 is the g.f. for A002294. - Robert A. Russell, Oct 03 2025

p=6; Table[(Binomial[(p-1)n, n]/(((p-2)n+1)((p-2)n+2))-If[OddQ[n], If[OddQ[p], Binomial[(p-1)n/2, (n-1)/2]/n, (p+1)Binomial[((p-1)n-1)/2, (n-1)/2]/((p-2)n+2)-Binomial[((p-1)n+1)/2, (n-1)/2]/((p-1)n+1)], Binomial[(p-1)n/2, n/2]/((p-2)n+2)]+DivisorSum[GCD[p, n-1], EulerPhi[#]Binomial[((p-1)n+1)/#, (n-1)/#]/((p-1)n+1)&, #>1&])/2, {n, 4, 30}]

Cf. A221184{n-1} (oriented), A004127 (unoriented), A143546 (achiral), A389337 (asymmetric), A002294 (rooted), A389194 {5,oo}, A389562 {7,oo}.

Sequence in context: A367235 A355171 A266432 * A267243 A197570 A319884

Adjacent sequences: A369470 A369471 A369472 * A369474 A369475 A369476

easy,nonn

Robert A. Russell, Jan 23 2024

approved