A003155 Number of ways to halve an n X n chessboard.

1, 1, 1, 6, 15, 255, 1897, 92263, 1972653, 281035054, 17635484470, 7490694495750, 1405083604458437, 1789509008288411290

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

This is the number of ways to cut an n X n chessboard along grid lines into two identical pieces. In the case that n is odd the central square is first removed to ensure an even number of squares. Solutions that differ only by rotation or reflection are considered equivalent. - Andrew Howroyd, Apr 19 2016

References

• M. Gardner, The Unexpected Hanging and Other Mathematical Diversions. Simon and Schuster, NY, 1969, p. 189.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Illustration showing ways to quarter a 6x6 board

Crossrefs

Cf. A113900, A006067, A257952, A271741.

Formula

a(2n) = A113900(n). - Andrew Howroyd, Apr 19 2016

Extensions

a(10) corrected and a(11)-a(14) from Andrew Howroyd, Apr 19 2016