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A295223 Number of tilings of the n X n torus, using diagonal lines to connect the gridpoints. 2
1, 4, 18, 669 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..4.

Peter Kagey, The eighteen tilings of the 3 x 3 torus.

EXAMPLE

For n = 3, the following four tilings are considered equivalent:

*---*->-+---+   +---+->-*---*   *---*->-+---+   +---+->-+---+

| / | \ | \ |   | / | / | \ |   | \ | / | / |   | / | \ | \ |

*---*---+---+   +---+---*---*   *---*---+---+   *---*---+---+

^ / | / | \ ^ = ^ / | \ | \ ^ = ^ \ | / | \ ^ = ^ \ | / | / ^

+---+---+---+   +---+---+---+   +---+---+---+   *---*---+---+

| \ | / | / |   | \ | \ | / |   | / | \ | \ |   | \ | / | \ |

+---+->-+---+   +---+->-+---+   +---+->-+---+   +---+->-+---+

The transformations are horizontal reflection, shifting to the right, and shifting down.

CROSSREFS

Cf. A295229.

Sequence in context: A086400 A082022 A114574 * A173222 A156491 A287677

Adjacent sequences:  A295220 A295221 A295222 * A295224 A295225 A295226

KEYWORD

nonn,more

AUTHOR

Peter Kagey, Nov 17 2017

STATUS

approved

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Last modified January 20 22:57 EST 2020. Contains 331104 sequences. (Running on oeis4.)