A003155 - OEIS

A003155

Number of ways to halve an n X n chessboard.
(Formerly M4111)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

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

Table of n, a(n) for n=1..14.

Illustration showing ways to quarter a 6x6 board

FORMULA

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

CROSSREFS

Cf. A113900, A006067, A257952, A271741.

Sequence in context: A013230 A306342 A117062 * A335578 A199095 A235230

Adjacent sequences: A003152 A003153 A003154 * A003156 A003157 A003158