

A064941


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


5



1, 3, 26, 596, 38171, 7083827, 3852835452, 6200587517574, 29752897658253125, 427721252609771505989, 18479976131829456895423324, 2405174963192312814001570260392, 944597040906414962273553855513194341, 1120924326970482645724785944664901286951323
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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 nth term a graph with n X (n1) 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 (matrixtransfer) 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



