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
Keywords
Links
- 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
Extensions
a(7)-a(8) from Juris Cernenoks, Feb 27 2013
a(9)-a(14) from Andrew Howroyd, Apr 18 2016