

A321614


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


2



1, 4, 23, 106, 473, 1939, 7618, 28703, 105112, 375597, 1316944, 4544124, 15474559, 52108212, 173799309, 574908646, 1888125243, 6162032375, 19998659760, 64584817367, 207655073310, 665017743665
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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(n1)  54*a(n2) + 98*a(n3) + 17*a(n4)  346*a(n5) + 505*a(n6)  210*a(n7)  120*a(n8) + 126*a(n9)  27*a(n10) 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



