A396643 - OEIS

A396643

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

0, 4, 40, 372, 3464, 32832, 317220, 3117132, 31062664, 313127688, 3186613786, 32687245866, 337545932011

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OFFSET

1,2

COMMENTS

A390622(n) counts the fixed polynars with n cells (edge-connected unions of n axis-aligned 2 X 2 blocks glued at integer offsets, counted up to translation only). Those whose blocks all lie on a common even sublattice are exactly the 2 X enlargements 2P of the fixed n-ominoes P, and there are A001168(n) of these; this sequence counts the rest, namely the fixed polynars in which every tiling by 2 X 2 blocks uses at least one half-edge (one-step offset) gluing. This is the fixed analog of A397023 (the free case).

LINKS

Table of n, a(n) for n=1..13.

George Sicherman, Catalogue of Polynars.

Index entries for sequences related to polyominoes.

FORMULA

a(n) = A390622(n) - A001168(n).

EXAMPLE

a(2) = A390622(2) - A001168(2) = 6 - 2 = 4: of the six fixed polynars with 2 cells, the two aligned ones (2 X the horizontal and vertical dominoes) are excluded, leaving the four offset gluings.

a(3) = A390622(3) - A001168(3) = 46 - 6 = 40.

CROSSREFS

Cf. A390622 (fixed polynars), A001168 (fixed polyominoes), A397023 (free analog), A390621 (one-sided polynars), A390620, A000105.

Sequence in context: A220366 A220310 A246152 * A155641 A122652 A299867

Adjacent sequences: A396640 A396641 A396642 * A396644 A396645 A396646

KEYWORD

nonn,more

AUTHOR

Haoyang Xu, Jun 29 2026

STATUS

approved