cp's OEIS Frontend

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.

%I A213430 N0663 #41 Jul 20 2024 18:43:07
%S A213430 1,2,6,26,159,1347,15593,244173,5131436
%N 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.
%C A213430 A006455 is equivalent to this sequence without the nonincreasing condition on the row sums. - _Petros Hadjicostas_, Jul 20 2024
%D A213430 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 A213430 Hansraj Gupta, Number of topologies in a finite set, Research Bulletin of the Panjab University, Vol. 19 (1968), p. 240. MR0268836.
%D A213430 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%H A213430 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 A213430 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a213/A213430.java">Java program</a>
%H A213430 Wikipedia, <a href="https://en.wikipedia.org/wiki/Finite_topological_space">Finite topological space</a>.
%H A213430 zbMATH, <a href="https://zbmath.org/0185.50503">Review of Gupta article</a>.
%Y A213430 Cf. A000798, A001035, A006455.
%K A213430 nonn,more
%O A213430 1,2
%A A213430 _N. J. A. Sloane_, Jun 11 2012
%E A213430 a(7) and new name from _Petros Hadjicostas_, Jul 20 2024
%E A213430 a(8)-a(9) from _Sean A. Irvine_, Jul 20 2024