%I #32 Feb 11 2019 21:21:15
%S 1,4,23,106,473,1939,7618,28703,105112,375597,1316944,4544124,
%T 15474559,52108212,173799309,574908646,1888125243,6162032375,
%U 19998659760,64584817367,207655073310,665017743665
%N Number of nonequivalent ways to place 2n nonattacking kings on a 4 X 2n chessboard under all symmetry operations of the rectangle.
%C A maximum of 2n nonattacking kings can be placed on a 4 X 2n chessboard.
%C Number of nonequivalent ways of placing 2n 2 X 2 tiles in an 5 X (2n+1) rectangle under all symmetry operations of the rectangle. - _Andrew Howroyd_, Dec 21 2018
%F a(n) = A231145(2*n+1, 2n).
%F Conjectures from _Colin Barker_, Dec 22 2018: (Start)
%F G.f.: (1 - 2*x)*(1 - 6*x + 17*x^2 - 18*x^3 - 2*x^4 + 7*x^5 + 6*x^6 - 3*x^7) / ((1 - x)^2*(1 - 3*x)^2*(1 - 3*x + x^2)*(1 - x - x^2)*(1 - 3*x^2)).
%F a(n) = 12*a(n-1) - 54*a(n-2) + 98*a(n-3) + 17*a(n-4) - 346*a(n-5) + 505*a(n-6) - 210*a(n-7) - 120*a(n-8) + 126*a(n-9) - 27*a(n-10) for n>9.
%F (End)
%Y Cf. A001787, A061593, A061594, A231145, A319096, A322284.
%K nonn,more
%O 0,2
%A _Anton Nikonov_, Dec 19 2018