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%I #36 May 26 2021 06:00:07
%S 1,6,36,412,9386,257318,8891854,379978716,19206532478,1120204619108,
%T 74113608972922,5483225594409823,448414229054798028,
%U 40154319792412218900,3906519894750904583838
%N Number of ways to place n nonattacking knights on an n X n board.
%C a(n) = A244081(n,n). - _Alois P. Heinz_, Jun 19 2014
%H V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 293.
%F a(n) ~ n^(2n)/n!*exp(-9/2). - _Vaclav Kotesovec_, Nov 29 2011
%t b[n_, l_] := b[n, l] = Module[{d, f, g, k}, d = Length[l]/3; f = False; Which[n == 0, 1, l[[1 ;; d]] == Array[f&, d], b[n - 1, Join[l[[d + 1 ;; 3*d]], Array[True&, d]]], True, For[k = 1, ! l[[k]], k++]; g = ReplacePart[l, k -> f];
%t If[k > 1, g = ReplacePart[g, 2*d - 1 + k -> f]];
%t If[k < d, g = ReplacePart[g, 2*d + 1 + k -> f]];
%t If[k > 2, g = ReplacePart[g, d - 2 + k -> f]];
%t If[k < d - 1, g = ReplacePart[g, d + 2 + k -> f]];
%t Expand[b[n, ReplacePart[l, k -> f]] + b[n, g]*x]]];
%t T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][ b[n, Array[True&, n*3]]];
%t a[n_] := T[n][[n + 1]];
%t Table[an = a[n]; Print["a(", n, ") = ", an]; an, {n, 1, 10}] (* _Jean-François Alcover_, Mar 29 2016, after _Alois P. Heinz_'s code for A244081 *)
%Y Cf. A172132, A172134, A172135, A172136, A178499, A244081.
%Y Cf. A244284, A201511, A201861, A201513, A141243.
%K nonn,nice,hard,more
%O 1,2
%A _Vaclav Kotesovec_, Dec 02 2011
%E a(11) from _Alois P. Heinz_, Jun 19 2014
%E a(12)-a(13) from _Vaclav Kotesovec_, Jun 21 2014
%E a(14) from _Vaclav Kotesovec_, Aug 26 2016
%E a(15) from _Vaclav Kotesovec_, May 26 2021
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