A352662 -id:A352662 - cp's OEIS frontend

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

Ulrich Schimke (ulrschimke(AT)aol.com)

A superqueen moves like a queen and a knight.

Superqueens are also called amazons.

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

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

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

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

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

A352661 Number of doubly symmetric characteristic solutions to the n-superqueens problem.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 0, 0, 12, 17, 0, 0, 60, 82

Offset: 1

Don Knuth, Mar 25 2022

Superqueens are also called amazons. They combine the moves of queen and knight.

			For n=12 the a(12)=2 solutions are
  +-------------------------+ +-------------------------+
  | . . . . A . . . . . . . | | . . . . A . . . . . . . |
  | . . . . . . . . . A . . | | . . . . . . . . . A . . |
  | . A . . . . . . . . . . | | . A . . . . . . . . . . |
  | . . . . . A . . . . . . | | . . . . . . A . . . . . |
  | . . . . . . . . . . . A | | . . . . . . . . . . . A |
  | . . . . . . . . A . . . | | . . . A . . . . . . . . |
  | . . . A . . . . . . . . | | . . . . . . . . A . . . |
  | A . . . . . . . . . . . | | A . . . . . . . . . . . |
  | . . . . . . A . . . . . | | . . . . . A . . . . . . |
  | . . . . . . . . . . A . | | . . . . . . . . . . A . |
  | . . A . . . . . . . . . | | . . A . . . . . . . . . |
  | . . . . . . . A . . . . | | . . . . . . . A . . . . |
  +-------------------------+ +-------------------------+

Martin Gardner, Fractal Music, Hypercards, and More, W H Freeman, 1991, page 238 (based on his column in Scientific American, June 1979).
D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3 (draft, March 2022).

A051224 = A352661 + A352662 + A352663.

A051223 = 2*A352661 + 4*A352662 + 8*A352663 (when n>1).

A352663 Number of asymmetric characteristic solutions to the n-superqueens problem.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 18, 231, 642, 4040, 25320, 166201, 1115373, 8060958, 61981118, 497224414

Offset: 1

Don Knuth, Mar 25 2022

			One of the a(11)=5 solutions is
  +-----------------------+
  | A . . . . . . . . . . |
  | . . . . A . . . . . . |
  | . . . . . . . . A . . |
  | . A . . . . . . . . . |
  | . . . . . A . . . . . |
  | . . . . . . . . . A . |
  | . . A . . . . . . . . |
  | . . . . . . A . . . . |
  | . . . . . . . . . . A |
  | . . . A . . . . . . . |
  | . . . . . . . A . . . |
  +-----------------------+
and the other four are obtained by wraparound shifts.

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

Cf. A051223, A051224, A352661, A352662.

cp's OEIS Frontend

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

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A352661 Number of doubly symmetric characteristic solutions to the n-superqueens problem.

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A352663 Number of asymmetric characteristic solutions to the n-superqueens problem.

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