A101454 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) ), divided by 2^n.

1, 0, 1, 0, 0, 6, 28, 0, 0, 911, 0, 16435, 107713

Offset

0,6

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.

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

Table of n, a(n) for n=0..12.

Yuh-Pyng Shieh, Complete Mappings

Example

a(5)=6 because the number of inequivalent solutions to toroidal 41-queen problem under R45 is 192 and 192 / (2^5) = 6.

Crossrefs

Cf. A007705, A057126.

Sequence in context: A276412 A006174 A064810 * A091911 A215896 A211679

Adjacent sequences: A101451 A101452 A101453 * A101455 A101456 A101457

Keyword

hard,nonn

Author

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

Status

approved