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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.
(Formerly N0663)
1

%I N0663 #41 Jul 20 2024 18:43:07

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

%N 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.

%C A006455 is equivalent to this sequence without the nonincreasing condition on the row sums. - _Petros Hadjicostas_, Jul 20 2024

%D 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.

%D Hansraj Gupta, Number of topologies in a finite set, Research Bulletin of the Panjab University, Vol. 19 (1968), p. 240. MR0268836.

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

%H Hansraj Gupta, <a href="/A213430/a213430.pdf">Number of topologies in a finite set</a>, Research Bulletin of the Panjab University, Vol. 19 (1968), p. 240. MR0268836.

%H Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a213/A213430.java">Java program</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Finite_topological_space">Finite topological space</a>.

%H zbMATH, <a href="https://zbmath.org/0185.50503">Review of Gupta article</a>.

%Y Cf. A000798, A001035, A006455.

%K nonn,more

%O 1,2

%A _N. J. A. Sloane_, Jun 11 2012

%E a(7) and new name from _Petros Hadjicostas_, Jul 20 2024

%E a(8)-a(9) from _Sean A. Irvine_, Jul 20 2024