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URL: https://oeis.org/A351616

⇱ A351616 - OEIS

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A351616

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

4

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

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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