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

0,2

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

Links

Table of n, a(n) for n=0..21.

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)

Crossrefs

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

Sequence in context: A122738 A038381 A241777 * A082970 A197868 A017973

Adjacent sequences: A321611 A321612 A321613 * A321615 A321616 A321617

Keyword

nonn,more

Author

Anton Nikonov, Dec 19 2018

Status

approved