A101453 Number of inequivalent solutions to toroidal (8n+1)-queen problem under the symmetry operator R45(x,y)=( (x-y)/sqrt(2), (x+y)/sqrt(2) ).

1, 0, 4, 0, 0, 192, 1792, 0, 0, 466432, 0, 33658880, 441192448

Offset: 0

Author

Yuh-Pyng Shieh, Yung-Luen Lan, Jieh Hsiang (arping(AT)turing.csie.ntu.edu.tw), Jan 19 2005

Keywords

• hard
• nonn

Comments

The R45 operator is not valid on toroidal N-queen problem if 2 is not a perfect square modulo N. For example, a(3)=0 is because 2 is not a perfect square modulo 25. see A057126. Toroidal N-queen problem has no fixed points under R45 if N is not equal to 8k+1 for some integer k.

Examples

			a(5)=6 because the number of inequivalent solutions to toroidal 41-queen problem under R45 is 192.
		

References

• Jieh Hsiang, Yuh-Pyng Shieh and YaoChiang Chen, "The Cyclic Complete Mappings Counting Problems", PaPS: Problems and Problem Sets for ATP Workshop in conjunction with CADE-18 and FLoC 2002, Copenhagen, Denmark, 2002/07/27-08/01.

Links

• Yuh-Pyng Shieh, Complete Mappings

Crossrefs

Cf. A007705, A057126.