|
%I #47 Aug 16 2021 14:48:30
%S 1,2,2,8,20,94,438,2766,19480,163058,1546726,16598282,197708058,
%T 2586423174,36769177348,563504645310,9248221393974,161670971937362,
%U 2996936692836754,58689061747521430,1210222434323163704,26204614054454840842,594313769819021397534,14086979362268860896282
%N Number of ways to place n nonattacking empresses on an n X n board.
%C An empress moves like a rook and a knight.
%H Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, <a href="https://arxiv.org/abs/1905.12364">Separators - a new statistic for permutations</a>, arXiv:1905.12364 [math.CO], 2019.
%H Eli Bagno, Estrella Eisenberg, Shulamit Reches, and Moriah Sigron, <a href="http://ecajournal.haifa.ac.il/Volume2021/ECA2021_S2A21.pdf">On the Sparseness of the Downsets of Permutations via Their Number of Separators</a>, Enumerative Combinatorics and Applications (2021) Vol. 1, No. 3, Article #S2R21.
%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p.685 and 636.
%H W. Schubert, <a href="http://web.archive.org/web/20130708134012/http://m29s20.vlinux.de/~wschub/nqueen.html">N-Queens page</a>
%F Asymptotics (Vaclav Kotesovec, Jan 26 2011): a(n)/n! -> 1/e^4.
%F General asymptotic formulas for number of ways to place n nonattacking pieces rook + leaper[r,s] on an n X n board:
%F a(n)/n! -> 1/e^2 for 0<r=s
%F a(n)/n! -> 1/e^4 for 0<r<s
%Y Cf. A201513, A000170, A002465, A201540.
%Y Cf. A185085, A051223, A244284, A201511, A201861, A137774, A245011.
%Y Cf. A218244, A002464, A110128, A117574, A089222, A002493.
%K nonn,nice,hard
%O 1,2
%A _Vaclav Kotesovec_, Jan 27 2011
%E Terms a(16)-a(17) from _Vaclav Kotesovec_, Feb 06 2011
%E Terms a(18)-a(19) from Wolfram Schubert, Jul 24 2011
%E Terms a(20)-a(24) (computed by Wolfram Schubert), _Vaclav Kotesovec_, Aug 25 2012
|
