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, 100027906

Offset

1,1

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.

Links

Table of n, a(n) for n=1..10.

B. Shtylla and L. Zulli, Ortho-projection graphs

Example

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].

Crossrefs

Cf. A081081, A081082.

Sequence in context: A076132 A371999 A047142 * A395025 A370070 A109460

Adjacent sequences: A081077 A081078 A081079 * A081081 A081082 A081083

Keyword

hard,more,nonn

Author

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

Extensions

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

a(10) from Sean A. Irvine, Oct 10 2025

Status

approved