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

1,11

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

Table of n, a(n) for n=1..26.

D. Bill, Durango Bill's The N-Queens Problem

W. Schubert, N-Queens page

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

Crossrefs

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

Sequence in context: A302926 A121796 A379997 * A062818 A154079 A160633

Adjacent sequences: A051221 A051222 A051223 * A051225 A051226 A051227

Keyword

nonn,more

Author

Ulrich Schimke (ulrschimke(AT)aol.com)

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

Status

approved