cp's OEIS Frontend

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

%I A051224 #28 Feb 15 2024 06:25:46
%S A051224 1,0,0,0,0,0,0,0,0,1,6,22,239,653,4089,25411,166463,1115871,8062150,
%T A051224 61984976,497236090,4261538564,38352532487,360400504834,3518014210402,
%U A051224 35752764285788
%N A051224 Number of ways of placing n nonattacking superqueens on n X n board (symmetric solutions count only once).
%C A051224 A superqueen moves like a queen and a knight.
%C A051224 Superqueens are also called amazons.
%D A051224 D. E. Knuth, The Art of Computer Programming, Section 7.2.2.3 (draft, March 2022)
%H A051224 D. Bill, <a href="http://www.durangobill.com/N_Queens.html">Durango Bill's The N-Queens Problem</a>
%H A051224 W. Schubert, <a href="https://web.archive.org/web/20160410085823/http://m29s20.vlinux.de/~wschub/nqueen.html">N-Queens page</a>
%F A051224 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
%Y A051224 Cf. A051223, A002562, A352661, A352662, A352663.
%K A051224 nonn,more
%O A051224 1,11
%A A051224 Ulrich Schimke (ulrschimke(AT)aol.com)
%E A051224 a(20) from Bill link added Jul 25 2006
%E A051224 a(21)..a(22) added from Bill's website. _Max Alekseyev_, Oct 19 2008
%E A051224 Added formula and a(23)..a(25) derived by formula. _W. Schubert_, Nov 29 2009
%E A051224 Added a(26). _W. Schubert_, Jan 18 2011