A393744 Number of free polyominoes in the {8,8} tessellation of the hyperbolic plane.

1, 1, 1, 4, 21, 183, 1918, 22908, 290511, 3844666, 52453581, 733300683, 10458157796, 151676284707, 2231506564296

Offset

0,4

Comments

For unoriented (free) polyominoes, chiral pairs are counted as one. - Robert A. Russell, Apr 04 2026

Links

Table of n, a(n) for n=0..14.

Formula

a(n) = P{p,q}(n) (the number of {p,q} polyominoes of size n) is equal to P{p,oo}(n) for n <= q; also P{p,q}(q+1) = P{p,oo}(q+1) + floor((p-1)/2) - floor((3+q(p-2))/2). In this case, p=8, q=8 and P{p,oo} = A389937.

a(n) = A394862(n) - A394863(n) = (A394862(n) + A394864(n)) / 2 = A394863(n) + A394864(n). - Robert A. Russell, Apr 04 2026

Crossrefs

Cf. A393739, A393740, A393741, A393742, A393743, A394862 (oriented), A394863 (chiral), A394864 (achiral), A389937 {8,oo}.

Sequence in context: A393741 A393742 A393743 * A389937 A221370 A224500

Adjacent sequences: A393741 A393742 A393743 * A393745 A393746 A393747

Keyword

nonn,hard,more

Author

John Mason, Érika Roldán, and Rosemberg Toalá-Enríquez, Mar 02 2026

Extensions

a(13) from Robert A. Russell, Apr 04 2026 using programs at A394862 and A394864.

a(14) from John Mason, May 18 2026

Status

approved