A113900 Number of partitions of 2n X 2n checkerboard into two congruent edgewise-connected sets, counting partitions equal under rotation or reflection only once.

1, 6, 255, 92263, 281035054, 7490694495750, 1789509008288411290

Offset

1,2

References

Howard Eves, A Survey of Geometry, 1963, p265.

Links

Table of n, a(n) for n=1..7.

Giovanni Resta, Illustrations for a(2) = 6 and a(3) = 255.

Example

All partitions are radially symmetric, hence can be identified by half the cut. The solution for 4 X 4 follows, with coordinates of starting point and direction of each subsequent incremental cut (North is positive Y).
(1,0)NNNES (1,0)NNE (1,0)NEN (1,0)NEENW (2,0)NN (2,0)NENW total = 6

Crossrefs

Cf. A064941, A068392, A257952.

Sequence in context: A320979 A279869 A271501 * A053944 A362713 A324091

Adjacent sequences: A113897 A113898 A113899 * A113901 A113902 A113903

Keyword

nonn,more

Author

Joseph Sardinha (jsardi3(AT)juno.com), Jan 29 2006

Extensions

a(5) corrected by Giovanni Resta, May 14 2015

New value of a(5) confirmed by and additional values a(6) and a(7) from Andrew Howroyd, Apr 13 2016

Status

approved