cp's OEIS Frontend

A201540 Number of ways to place n nonattacking knights on an n X n board.

%I A201540 #36 May 26 2021 06:00:07
%S A201540 1,6,36,412,9386,257318,8891854,379978716,19206532478,1120204619108,
%T A201540 74113608972922,5483225594409823,448414229054798028,
%U A201540 40154319792412218900,3906519894750904583838
%N A201540 Number of ways to place n nonattacking knights on an n X n board.
%C A201540 a(n) = A244081(n,n). - _Alois P. Heinz_, Jun 19 2014
%H A201540 V. Kotesovec, <a href="https://oeis.org/wiki/User:Vaclav_Kotesovec">Non-attacking chess pieces</a>, 6ed, 2013, p. 293.
%F A201540 a(n) ~ n^(2n)/n!*exp(-9/2). - _Vaclav Kotesovec_, Nov 29 2011
%t A201540 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 A201540      If[k > 1, g = ReplacePart[g, 2*d - 1 + k -> f]];
%t A201540      If[k < d, g = ReplacePart[g, 2*d + 1 + k -> f]];
%t A201540      If[k > 2, g = ReplacePart[g, d - 2 + k -> f]];
%t A201540      If[k < d - 1, g = ReplacePart[g, d + 2 + k -> f]];
%t A201540      Expand[b[n, ReplacePart[l, k -> f]] + b[n, g]*x]]];
%t A201540 T[n_] := Function[p, Table[Coefficient[p, x, i], {i, 0, Exponent[p, x]}]][ b[n, Array[True&, n*3]]];
%t A201540 a[n_] := T[n][[n + 1]];
%t A201540 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 A201540 Cf. A172132, A172134, A172135, A172136, A178499, A244081.
%Y A201540 Cf. A244284, A201511, A201861, A201513, A141243.
%K A201540 nonn,nice,hard,more
%O A201540 1,2
%A A201540 _Vaclav Kotesovec_, Dec 02 2011
%E A201540 a(11) from _Alois P. Heinz_, Jun 19 2014
%E A201540 a(12)-a(13) from _Vaclav Kotesovec_, Jun 21 2014
%E A201540 a(14) from _Vaclav Kotesovec_, Aug 26 2016
%E A201540 a(15) from _Vaclav Kotesovec_, May 26 2021