A270858 Number of n X n checkered tori (see A179043) with at least one 0 and at least one 1 in each row and each column.

0, 1, 14, 1446, 705366, 1304451482

Offset

1,3

Comments

Let us denote by Qn the set of all n X n binary matrices with at least one 0 and at least one 1 in each row and each column. Let A,B belong to Qn. We will say that A and B are equivalent if B is obtained from A as a result of a sequential cyclic move of the last row or column at a first position. [Please rewrite that sentence!] It's easy to see that this defines an equivalence relation. The sequence gives the number of equivalence classes. The elements of the factor-set Qn/~ are relevant in the textile industry.

Links

Table of n, a(n) for n=1..6.

K. Yordzhev, An example for the use of bitwise operations in programming, Mathematics and education in mathematics, v. 38 (2009), 196-202, also arXiv:1201.1468 [cs.OH], 2012.

K. Yordzhev, H. Kostadinova, Mathematical Modelling in the Textile Industry Bulletin of Mathematical Sciences & Applications, Vol. 1, No. 1 (2012), pp. 20 -35.

Crossrefs

Cf. A179043.

Sequence in context: A204698 A240773 A131582 * A160246 A145693 A279326

Adjacent sequences: A270855 A270856 A270857 * A270859 A270860 A270861

Keyword

nonn,more

Author

Krasimir Yordzhev, Mar 24 2016

Status

approved