A064941 Quartering a 2n X 2n chessboard (reference A257952) considering only the 90-deg rotationally symmetric results (omitting results with only 180-deg symmetry).

1, 3, 26, 596, 38171, 7083827, 3852835452, 6200587517574, 29752897658253125, 427721252609771505989, 18479976131829456895423324, 2405174963192312814001570260392, 944597040906414962273553855513194341, 1120924326970482645724785944664901286951323

Offset

1,2

Links

Table of n, a(n) for n=1..14.

Walter Gilbert, Chessboard quartering; includes generating program.

Formula

No formula known. However, the subset of solutions consisting of "tiles" with minimum edge lengths from a corner of the board to the center is A001700.

This sequence can be computed by counting paths in a graph. To compute the n-th term a graph with n X (n-1) vertices is required. Each graph vertex corresponds to 4 intersections between grid lines on the chessboard and graph edges correspond to ways of cutting the board along the grid lines. Frontier (matrix-transfer) graph path counting methods can then be applied to the graph to get the actual count. - Andrew Howroyd, Apr 18 2016

Crossrefs

Cf. A257952, A113900.

Sequence in context: A059511 A112676 A103112 * A112612 A129430 A005156

Adjacent sequences: A064938 A064939 A064940 * A064942 A064943 A064944

Keyword

nonn

Author

Walter Gilbert (Walter(AT)Gilbert.net), Oct 28 2001

Extensions

a(7)-a(8) from Juris Cernenoks, Feb 27 2013

a(9)-a(14) from Andrew Howroyd, Apr 18 2016

Status

approved