cp's OEIS Frontend

A005991 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).

%I A005991 M1582 #21 Jan 10 2024 23:56:02
%S A005991 2,6,12,20,30,43
%N A005991 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 A005991 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A005991 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 A005991 <a href="/index/Mat#binmat">Index entries for sequences related to binary matrices</a>
%F A005991 a(n) = A003509(n + 1) - 1. - _Sean A. Irvine_, Jun 04 2015
%e A005991 Since k(2) = 2 then a(1) = 2
%e A005991 Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6
%e A005991 Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12
%e A005991 Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20
%e A005991 Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30
%e A005991 Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43
%Y A005991 Cf. A003509 (index of first term), A155934.
%K A005991 nonn,more
%O A005991 1,1
%A A005991 _N. J. A. Sloane_
%E A005991 Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008