A051224 Number of ways of placing n nonattacking superqueens on n X n board (symmetric solutions count only once).

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

Offset: 1

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

Keywords

• nonn
• more

Comments

A superqueen moves like a queen and a knight.

Superqueens are also called amazons.

References

• D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3 (draft, March 2022)

Links

• D. Bill, Durango Bill's The N-Queens Problem
• W. Schubert, N-Queens page

Crossrefs

Cf. A051223, A002562, A352661, A352662, A352663.

Formula

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

Extensions

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

Added a(26). W. Schubert, Jan 18 2011