login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A033148
Number of rotationally symmetric solutions for queens on n X n board.
7
1, 0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 8, 8, 0, 0, 64, 128, 0, 0, 480, 704, 0, 0, 3328, 3264, 0, 0, 32896, 43776, 0, 0, 406784, 667904, 0, 0, 5845504, 8650752, 0, 0, 77184000, 101492736, 0, 0, 1261588480, 1795233792, 0, 0, 21517426688, 35028172800, 0, 0, 406875119616, 652044443648, 0, 0, 8613581094912, 12530550128640, 0, 0, 194409626533888, 291826098503680, 0, 0
OFFSET
1,4
COMMENTS
From Don Knuth, Jul 17 2015: (Start)
Ahrens proved that a(n)=0 unless n=4k or 4k+1. He also proved that in the latter case, a(n) is a multiple of 2^k. He found all solutions when n was less than 20.
Kraitchik carried the calculations further (for n less than 28). In his book he tabulated only the values a(n)/2^k. He had correct entries for n=21 and n=25, but his values for n=20 and n=24 were 1 too small -- of course he had calculated everything by hand! (End)
REFERENCES
W. Ahrens, Mathematische Unterhaltungen und Spiele, 2nd edition, volume 1, Teubner, 1910, pages 249-258.
Maurice Kraitchik, Le problème des reines, Bruxelles: L'Échiquier, 1926, page 18.
LINKS
Tricia M. Brown, Kaleidoscopes, Chessboards, and Symmetry, Journal of Humanistic Mathematics, Volume 6 Issue 1 ( January 2016), pages 110-126.
P. Capstick and K. McCann, The problem of the n queens, apparently unpublished, no date (circa 1990?) [Scanned copy]
Gheorghe Coserea, Solutions for n=20.
Gheorghe Coserea, Solutions for n=24.
CROSSREFS
KEYWORD
nonn,hard
AUTHOR
Miklos SZABO (mike(AT)ludens.elte.hu)
EXTENSIONS
More terms from Jieh Hsiang and YuhPyng Shieh (arping(AT)turing.csie.ntu.edu.tw), May 20 2002
STATUS
approved