Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #27 Aug 07 2024 09:20:33
%S 1,32,408,3600,26040,166368,976640,5392704,28432288,144605184,
%T 714611200,3449705600,16333065216,76081271168,349524164224,
%U 1586790140800,7130144209024,31752978219904,140298397039232,615604372260736
%N Number of ways to place 3n nonattacking kings on a 6 X 2n chessboard.
%H Vincenzo Librandi, <a href="/A061594/b061594.txt">Table of n, a(n) for n = 0..1000</a>
%H D. E. Knuth, <a href="http://www-cs-faculty.stanford.edu/~knuth/preprints.html">Nonattacking kings on a chessboard</a>, 1994.
%H Vaclav Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Number of ways of placing non-attacking queens and kings on boards of various sizes</a> [_Vaclav Kotesovec_, Feb 06 2010]
%H H. S. Wilf, <a href="https://doi.org/10.37236/1197">The problem of the kings</a>, Elec. J. Combin. 2, 1995.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (19, -148, 604, -1364, 1644, -928, 192).
%F G.f.: (1+13x-52x^2-20x^3+60x^4-20x^5)/((1-3x)(1-4x)^2(1-4x+2x^2)^2).
%F Explicit formula: (231n-2377)*4^n - 384*3^n + (1953*sqrt(2)/2+1381+(35*sqrt(2)+99/2)*n)*(2+sqrt(2))^n + (1381-1953*sqrt(2)/2+(99/2-35*sqrt(2))*n)*(2-sqrt(2))^n. - _Vaclav Kotesovec_, Feb 06 2010
%o (PARI) a(n)=polcoeff((1+13*x-52*x^2-20*x^3+60*x^4-20*x^5)/((1-3*x)*(1-4*x)^2*(1-4*x+2*x^2)^2)+x*O(x^n),n)
%Y Column k=3 of A350819.
%Y Cf. A001787, A061593.
%Y Equals 231*A002697(n+1) - 2608*A000302(n) - 384*A000244(n) + 1103*A007070(n-1) + 780*A006012(n+1) + (n+1)*(17*A048580(n) + 12*A007070(n+1)).
%K nonn,nice
%O 0,2
%A Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), May 22 2001
%E Corrected data by _Vincenzo Librandi_, Oct 12 2011