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A051224
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Number of ways of placing n nonattacking superqueens on n X n board (symmetric solutions count only once).
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9
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1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 22, 239, 653, 4089, 25411, 166463, 1115871, 8062150, 61984976, 497236090, 4261538564, 38352532487, 360400504834, 3518014210402, 35752764285788
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OFFSET
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1,11
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COMMENTS
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A superqueen moves like a queen and a knight.
Superqueens are also called amazons.
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REFERENCES
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D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3 (draft, March 2022)
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LINKS
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FORMULA
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a(n) = (1/8) * (Q(n) + P(n) + 2 * R(n)), where Q(n) = A051223(n) [all solutions], P(n) [point symmetric solutions (180 degrees)] and R(n) [rotationally symmetric solutions (90 degrees)]. This formula has the same structure as the formula for A002562. There seem to be no OEIS sequences (yet) for P(n) and R(n). See the N-Queens page link. - W. Schubert, Nov 29 2009
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CROSSREFS
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KEYWORD
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nonn,more
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AUTHOR
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Ulrich Schimke (ulrschimke(AT)aol.com)
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EXTENSIONS
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a(20) from Bill link added Jul 25 2006
a(21)..a(22) added from Bill's website. Max Alekseyev, Oct 19 2008
Added formula and a(23)..a(25) derived by formula. W. Schubert, Nov 29 2009
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STATUS
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approved
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