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 A319096 Number of nonequivalent ways to place n^2 nonattacking kings on a 2n X 2n chessboard under all symmetry operations of the square. 2
 1, 14, 459, 35312, 4072108, 638653285, 128441726634, 31872148398195, 9490641145219266, 3321018871480028710 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS A maximum of n^2 nonattacking kings may be placed on a 2n X 2n chessboard. LINKS FORMULA a(n) = A236679(2n+1, n^2). EXAMPLE For n = 2 there are a(2) = 14 distinct solutions from 79 that will not be repeated at all possible turns and reflections. ------------ 1.                  2. _________________   _________________ | * |   | * |   |   | * |   | * |   | |   |   |   |   |   |   |   |   |   | | * |   | * |   |   | * |   |   | * | |   |   |   |   |   |   |   |   |   | ------------ 3.                  4. _________________   _________________ | * |   | * |   |   | * |   | * |   | |   |   |   |   |   |   |   |   |   | | * |   |   |   |   |   | * |   | * | |   |   |   | * |   |   |   |   |   | ------------ 5.                  6. _________________   _________________ | * |   | * |   |   | * |   | * |   | |   |   |   |   |   |   |   |   |   | |   | * |   |   |   |   |   | * |   | |   |   |   | * |   | * |   |   |   | ------------ 7.                  8. _________________   _________________ | * |   | * |   |   | * |   | * |   | |   |   |   |   |   |   |   |   |   | |   |   |   | * |   |   |   |   |   | | * |   |   |   |   | * |   | * |   | ------------ 9.                  10. _________________   _________________ | * |   | * |   |   | * |   | * |   | |   |   |   |   |   |   |   |   |   | |   |   |   |   |   |   |   |   | * | | * |   |   | * |   |   | * |   |   | ------------ 11.                 12. _________________   _________________ | * |   | * |   |   | * |   |   | * | |   |   |   |   |   |   |   |   |   | |   |   |   |   |   |   | * |   |   | |   | * |   | * |   |   |   |   | * | ------------ 13.                 14. _________________   _________________ | * |   |   | * |   |   | * |   |   | |   |   |   |   |   |   |   |   | * | |   |   |   |   |   | * |   |   |   | | * |   |   | * |   |   |   | * |   | ------------ CROSSREFS Cf. A018807 (rotations and reflections considered distinct). Cf. A137432 (on cylindrical chessboard). Cf. A236679, A322284, A321614. Sequence in context: A201546 A305115 A282245 * A297548 A215787 A005790 Adjacent sequences:  A319093 A319094 A319095 * A319097 A319098 A319099 KEYWORD nonn,more AUTHOR Anton Nikonov, Dec 21 2018 EXTENSIONS a(4)-a(10) from Andrew Howroyd, Dec 21 2018 STATUS approved

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Last modified November 29 18:41 EST 2021. Contains 349416 sequences. (Running on oeis4.)