A395329 Number of one-sided polynars with n cells that are not the 2 X enlargement of a one-sided n-omino.

0, 2, 11, 105, 878, 8321, 79418, 780436, 7766817, 78293570, 796665063, 8171931384

Offset

1,2

Comments

A390621(n) counts the one-sided polynars with n cells (edge-connected unions of n axis-aligned 2 X 2 blocks glued at integer offsets, counted up to rotation only). Those whose blocks all lie on a common even sublattice are exactly the 2 X enlargements 2P of the one-sided n-ominoes P, and there are A000988(n) of these; this sequence counts the rest, namely the one-sided polynars in which every tiling by 2 X 2 blocks uses at least one half-edge (one-step offset) gluing. This is the one-sided analog of A397023 (the free case).

Links

Table of n, a(n) for n=1..12.

George Sicherman, Catalogue of Polynars.

Index entries for sequences related to polyominoes.

Formula

a(n) = A390621(n) - A000988(n).

Example

a(2) = A390621(2) - A000988(2) = 3 - 1 = 2: the aligned 2 X 4 rectangle (= 2 X the domino) is excluded, and the single offset octomino (two 2 X 2 blocks meeting along a half edge) is chiral, so it contributes two one-sided polynars.
a(3) = A390621(3) - A000988(3) = 13 - 2 = 11.

Crossrefs

Cf. A390621 (one-sided polynars), A000988 (one-sided polyominoes), A397023 (free analog), A390622 (fixed polynars), A390620, A000105.

Sequence in context: A343896 A111535 A268294 * A364338 A379446 A375457

Adjacent sequences: A395326 A395327 A395328 * A395330 A395331 A395332

Keyword

nonn,more,new

Author

Haoyang Xu, Jun 29 2026

Status

approved