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#13 by N. J. A. Sloane at Sat Sep 12 11:00:25 EDT 2015
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| LINKS
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V. Kotesovec, <a href="httphttps://web.telecomoeis.czorg/vaclav.kotesovecwiki/math.htmUser:Vaclav_Kotesovec">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)
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Discussion
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| Sat Sep 12
| 11:00
| OEIS Server: https://oeis.org/edit/global/2459
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#12 by Vaclav Kotesovec at Tue Mar 04 06:29:59 EST 2014
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#11 by Vaclav Kotesovec at Tue Mar 04 06:29:42 EST 2014
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| FORMULA
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a(n)=2^n*n!*Sum[Binomial[n,i]^3,{i,0,n}]}].
Asymptotic: a(n) ~ 2^(4n+1)*(n-1)!/piPi/sqrt(3) ~ 2^(4n+1)*n^n/e^exp(n*)*sqrt(2/(3*piPi*n)))).
Recurrence: a(n) = ((14*n^2-14*n+4)*a(n-1) + 32*(n-1)^3*a(n-2))/n.
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| STATUS
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approved
editing
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#10 by Joerg Arndt at Sun Jun 02 13:18:19 EDT 2013
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#9 by Vincenzo Librandi at Sun Jun 02 13:00:25 EDT 2013
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#8 by Vincenzo Librandi at Sun Jun 02 12:42:07 EDT 2013
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| LINKS
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V. Kotesovec, <a href="http://web.telecom.cz/vaclav.kotesovec/math.htm">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)
V. Kotesovec, <a href="http://web.telecom.cz/vaclav.kotesovec/math.htm">Number of ways of placing non-attacking queens, kings, bishops and knights</a> (in English and Czech)
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#7 by Vincenzo Librandi at Sun Jun 02 12:41:33 EDT 2013
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| NAME
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Number of ways to place n nonattacking bishops on an 2n x 2n toroidal board.
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| LINKS
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Vincenzo Librandi, <a href="/A189791/b189791.txt">Table of n, a(n) for n = 1..200</a>
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| CROSSREFS
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Cf. A189790, A002465, A000172.
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| STATUS
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approved
editing
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#6 by Russ Cox at Fri Mar 30 19:00:54 EDT 2012
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| AUTHOR
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_Vaclav Kotesovec (kotesovec(AT)chello.cz), _, Apr 27 2011
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Discussion
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| Fri Mar 30
| 19:00
| OEIS Server: https://oeis.org/edit/global/319
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#5 by T. D. Noe at Fri Apr 29 14:26:15 EDT 2011
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#4 by Joerg Arndt at Fri Apr 29 05:43:11 EDT 2011
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