A321614 Number of nonequivalent ways to place 2n nonattacking kings on a 4 X 2n chessboard under all symmetry operations of the rectangle.

1, 4, 23, 106, 473, 1939, 7618, 28703, 105112, 375597, 1316944, 4544124, 15474559, 52108212, 173799309, 574908646, 1888125243, 6162032375, 19998659760, 64584817367, 207655073310, 665017743665

Offset: 0

Author

Anton Nikonov, Dec 19 2018

Keywords

• nonn
• more

Comments

A maximum of 2n nonattacking kings can be placed on a 4 X 2n chessboard.

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

Crossrefs

Cf. A001787, A061593, A061594, A231145, A319096, A322284.

Formula

a(n) = A231145(2*n+1, 2n).

Conjectures from Colin Barker, Dec 22 2018: (Start)

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)).

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.

(End)