OFFSET
1,2
COMMENTS
The three sequences A054500/A054501/A054502 are used to classify solutions to the problem of "Nonattacking queens on a 2n+1 X 2n+1 toroidal board" by their symmetry; solutions are considered equivalent iff they differ only by rotation, reflection or torus shift.
For brevity, let i(n) = A054500(n) (indicator sequence), m(n) = A054501(n) (multiplicity) and c(n) = A054502(n) (count).
i(n) = k means that there are solutions for the k X k board and that m(n) and c(n) refer to it. There are c(n) inequivalent solutions which may be extended to m(n) different representations each (i.e., m(n) permutations).
REFERENCES
A. P. Street and R. Day, Sequential binary arrays II: Further results on the square grid, pp. 392-418 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982 (for getting equivalence classes).
LINKS
Manuel Kauers and Christoph Koutschan, Guessing with Little Data, arXiv:2202.07966 [cs.SC], 2022.
I. Rivin, I. Vardi and P. Zimmermann, The n-queens problem, Amer. Math.Monthly, 101 (1994), 629-639 (for finding the solutions).
EXAMPLE
CROSSREFS
KEYWORD
nonn,nice,hard
AUTHOR
EXTENSIONS
More terms from Matthias Engelhardt, Jan 11 2001
STATUS
approved