A213430 The number of n X n upper triangular (0,1)-matrices M with all diagonal entries 1 such that M = f(M^2) and sum(row 1) >= sum(row 2) >= ... >= sum(row n-1) >= sum(row n) = 1 and f maps any nonzero entry to 1.

1, 2, 6, 26, 159, 1347, 15593, 244173, 5131436

Offset: 1

Author

N. J. A. Sloane, Jun 11 2012

Keywords

• nonn
• more

Comments

A006455 is equivalent to this sequence without the nonincreasing condition on the row sums. - Petros Hadjicostas, Jul 20 2024

References

• Collected papers of Professor Hansraj Gupta. Edited by R. J. Hans-Gill and Madhu Raka. Ramanujan Mathematical Society Collected Works Series, 3. See pp. 554-564.
• Hansraj Gupta, Number of topologies in a finite set, Research Bulletin of the Panjab University, Vol. 19 (1968), p. 240. MR0268836.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

Links

• Hansraj Gupta, Number of topologies in a finite set, Research Bulletin of the Panjab University, Vol. 19 (1968), p. 240. MR0268836.
• Sean A. Irvine, Java program
• Wikipedia, Finite topological space.
• zbMATH, Review of Gupta article.

Crossrefs

Cf. A000798, A001035, A006455.

Extensions

a(7) and new name from Petros Hadjicostas, Jul 20 2024

a(8)-a(9) from Sean A. Irvine, Jul 20 2024