A227787 The number of n X n tomographically balanced matrices.

1, 1, 1, 3, 31, 877, 107637, 66291089, 214925869109

Offset

1,4

Comments

A tomographically balanced matrix is a matrix whose entries are -1, 0, or +1, with the property that the sum over any row, any column, or any of the diagonal lines with slope plus-or-minus 1 is zero.

References

Donald E. Knuth, Satisfiability, Fascicle 6, volume 4 of The Art of Computer Programming, Addison-Wesley, 2015, pages 141 and 204-205, Exercise 105.

Links

Table of n, a(n) for n=1..9.

Example

For n=4 the three cases are 0000/0000/0000/0000, 0+-0/-00+/+00-/0-+0, and 0-+0/+00-/-00+/0+-0.

Crossrefs

Sequence in context: A317348 A144416 A362846 * A356673 A274592 A219266

Adjacent sequences: A227784 A227785 A227786 * A227788 A227789 A227790

Keyword

nonn,hard,more

Author

Don Knuth, Sep 23 2013

Extensions

a(9) from Bert Dobbelaere, Sep 14 2020

Status

approved