Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M1582 #21 Jan 10 2024 23:56:02
%S 2,6,12,20,30,43
%N Let k(m) denote the least integer such that every m X m (0,1)-matrix with exactly k(m) ones in each row and in each column contains a 2 X 2 submatrix without zeros. The sequence gives the index n of the last term in each string of equal entries in the {k(m)} sequence (see A155934).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H E. T. Wang and R. K. Guy, <a href="http://www.jstor.org/stable/2319052">Problem E2429</a>, Amer. Math. Monthly, 81 (1974), 1112-1113.
%H <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F a(n) = A003509(n + 1) - 1. - _Sean A. Irvine_, Jun 04 2015
%e Since k(2) = 2 then a(1) = 2
%e Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6
%e Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12
%e Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20
%e Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30
%e Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43
%Y Cf. A003509 (index of first term), A155934.
%K nonn,more
%O 1,1
%A _N. J. A. Sloane_
%E Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008