A225783 Triangle read by rows: T(n,m) is the number of n X m binary (0,1) matrices that represent perfect parity patterns.

0, 1, 0, 0, 2, 0, 0, 0, 0, 15, 0, 0, 4, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 240, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 112, 0, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0

Offset

1,5

Comments

An n X m matrix of zeros and ones is perfect if no row or column consists entirely of zeros (as counted in A183109). It is a parity pattern if every 0 is adjacent (vertically or horizontally) to an even number of 1s and every 1 is adjacent to an odd number of 1s.

Links

R. J. Mathar, Table of n, a(n) for n = 1..106

R. Chapman, D. E. Knuth, Problem 11243, Perfect parity patterns, Am. Math. Monthly 115 (7) (2008) p 668.

R. J. Mathar, Discussion and JAVA source code

Example

The T(5,3) = 4 perfect parity 5 X 3 patterns are
0 0 1
0 1 1
1 0 1
1 1 0
1 0 0
------
0 1 1
1 0 0
1 0 1
0 0 1
1 1 0
--------
1 0 0
1 1 0
1 0 1
0 1 1
0 0 1
--------
1 1 0
0 0 1
1 0 1
1 0 0
0 1 1

Crossrefs

Sequence in context: A230614 A230730 A299905 * A135468 A003196 A319581

Adjacent sequences: A225780 A225781 A225782 * A225784 A225785 A225786

Keyword

nonn,tabl

Author

R. J. Mathar, Jun 13 2014

Status

approved