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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 6 08:47 EST 2021. Contains 349563 sequences. (Running on oeis4.)