A351616 Number of free polyominoes with 2n squares, having 180-degree rotational symmetry about a vertex of a square, and no other symmetry.

0, 0, 1, 2, 12, 43, 174, 657, 2571, 9911, 38633, 150437, 588544, 2306204, 9061179, 35665587, 140648710, 555514177, 2197298561, 8702439446, 34506900216, 136972867380, 544237912916, 2164377093376, 8614630304437, 34314092253069, 136778054864067, 545565225736599, 2177428436636287

Offset

1,4

Comments

The sequence enumerates a subset of the polyominoes enumerated by A006747.

Links

Table of n, a(n) for n=1..29.

Toshihiro Shirakawa, Enumeration of Polyominoes up to Size N=59, arXiv:2510.22446 [math.CO], 2025.

Formula

a(n) = (A390655(n) - A351191(n/2)*2 - A351160(n)*2 - A234007(n/2)*2 - A346800(n/2))/4 where the terms with non-integer indices are set to 0. - John Mason, Dec 17 2025

Example

a(3)=1 because of:
   OOO
  OOO

Crossrefs

Cf. A006747, A234008, A351615, A390655, A351191, A351160, A234007, A346800.

Sequence in context: A301556 A055681 A296682 * A111389 A203278 A013704

Adjacent sequences: A351613 A351614 A351615 * A351617 A351618 A351619

Keyword

nonn

Author

John Mason, Feb 15 2022

Extensions

a(17)-a(25) from John Mason, Feb 26 2023

a(26)-a(29) from John Mason, Dec 17 2025

Status

approved