A234007 -id:A234007 - cp's OEIS frontend

A351142 Free chiral polyominoes with n squares, having 90-degree rotational symmetry about the center of a square of the underlying square matrix.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 0, 0, 3, 7, 0, 0, 14, 25, 0, 0, 55, 90, 0, 0, 216, 319, 0, 0, 816, 1136, 0, 0, 3098, 4088, 0, 0, 11711, 14868, 0, 0, 44462, 54526, 0, 0, 169213, 201527, 0, 0, 646441, 750169, 0, 0, 2477819, 2809931, 0, 0, 9530788, 10582370, 0, 0, 36768799, 40043785

Offset: 1

John Mason, Feb 02 2022

The sequence enumerates a subset of the polyominoes enumerated by A144553.

			a(12)=1 because of:
   O
   OOOO
   O O
  OOOO
     O

Cf. A000105, A144553, A234007.

For n multiple of 4, a(n) = A144553(n) - A234007(n/4); otherwise a(n) = A144553(n).

A060463 Number of open positions in the game Fair Share and Varied Pairs starting with n tokens.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 45, 56, 82, 111, 142, 194, 280, 343, 462, 589, 743, 946, 1232, 1505, 1921, 2381, 2983, 3664, 4536, 5521, 6796, 8287, 10064, 12209, 14848, 17856, 21600, 25949, 31127, 37244, 44542, 53040, 63197, 75071, 89025, 105418, 124707

Offset: 0

Jean Méhat, Apr 09 2001

E. R. Berlekamp, J. H. Conway, R. K. Guy, Winning Ways, Academic Press, 1982, pp. 359-363.

Sean A. Irvine, Java program (github)

a(16) onward corrected and more terms from Sean A. Irvine, Nov 22 2022

cp's OEIS Frontend

A351142 Free chiral polyominoes with n squares, having 90-degree rotational symmetry about the center of a square of the underlying square matrix.

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A060463 Number of open positions in the game Fair Share and Varied Pairs starting with n tokens.

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