A389939 Number of chiral pairs of asymmetric polyominoes with n octagonal cells of the hyperbolic regular tiling with Schläfli symbol {8,oo}.

11, 146, 1815, 22497, 289286, 3839641, 52438557, 733251173, 10458325094, 151683323684, 2231662273500, 33242246178585, 500542061456412, 7608837701945742, 116642747530853079, 1801638425854262512, 28016657945635270744, 438349148456038014918, 6896594434982945177961, 109055532806132438261294

Offset

4,1

Links

Table of n, a(n) for n=4..23.

Frank Harary, Edgar M. Palmer and Ronald C. Read, On the cell-growth problem for arbitrary polygons, Discr. Math. 11 (1975), 371-389.

Robert A. Russell, Stereographic projections of chiral pairs of asymmetric polyominoes with 4 cells.

Formula

G.f.: (7*G(z) - 3*G(z)^2 - 12*G(z^2) - 9*z*G(z^2)^4 + 8*G(z^4) + 8*z*G(z^4)^3 + 8*z^2*G(z^4)^4 + 8*z^3*G(z^4)^6) / 16, where G(z) = 1 + z*G(z)^7 is the g.f. for A002296.

Mathematica

Table[If[n<4, 0, (7Binomial[7n, n]/(6n+1)-3Binomial[7n+1, n]/(3n+1)-If[OddQ[n], 36Binomial[(7n-1)/2, (n-1)/2]/(3n+1)-If[OddQ[(n-1)/2], 32Binomial[(7n-1)/4, (n-3)/4], 16Binomial[(7n+1)/4, (n-1)/4]]/(n+1), 12Binomial[7n/2, n/2]/(3n+1)-If[OddQ[n/2], 64Binomial[(7n-2)/4, (n-2)/4], 16Binomial[7n/4, n/4]]/(3n+2)])/16], {n, 4, 40}]

Crossrefs

Cf. A389936 (oriented), A389937 (unoriented), A389938 (chiral), A143547 (achiral), A002296 (rooted), A389564 {7,oo}.

Sequence in context: A098310 A293610 A061613 * A093750 A194726 A383629

Adjacent sequences: A389936 A389937 A389938 * A389940 A389941 A389942

Keyword

nonn

Author

Robert A. Russell, Oct 21 2025

Status

approved