A081080 Number of n X n ortho-projection matrices over GF(2). Also, the number of labeled ortho-projection graphs on n vertices.

2, 4, 10, 38, 194, 1378, 13570, 188546, 3664898

Offset: 1

Author

B. Shtylla and L. Zulli (shtyllab(AT)lafayette.edu, zullil(AT)lafayette.edu), Mar 05 2003

Keywords

• hard
• more
• nonn

Comments

A matrix over GF(2) is an ortho-projection if and only if the matrix is symmetric and idempotent. A labeled ortho-projection graph is a labeled, undirected pseudograph without multiple edges and without multiple loops whose adjacency matrix is an ortho-projection matrix over GF(2). These matrices and graphs arise naturally in low-dimensional topology.

Examples

			a(2)=4 because there are four 2 X 2 ortho-projection matrices over GF(2), namely [0 0 / 0 0], [0 0 / 0 1], [1 0 / 0 0], [1 0 / 0 1].
		

References

• B. Shtylla and L. Zulli, Ortho-projection graphs, in preparation.

Links

• L. Zulli, Home Page [broken link]

Crossrefs

Cf. A081081, A081082.

Extensions

a(9) from Louis Zulli (zullil(AT)lafayette.edu), Aug 23 2004