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).

2, 6, 12, 20, 30, 43

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Examples

			Since k(2) = 2 then a(1) = 2
Since k(3) = k(4) = k(5) = k(6) = 3 then a(2) = 6
Since k(7) = k(8) = ... = k(12) = 4 then a(3) = 12
Since k(13) = k(14) = ... = k(20) = 5 then a(4) = 20
Since k(21) = k(22) = ... = k(30) = 6 then a(5) = 30
Since k(31) = k(32) = ... = k(43) = 7 then a(6) = 43
		

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• E. T. Wang and R. K. Guy, Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113.
• Index entries for sequences related to binary matrices

Crossrefs

Cf. A003509 (index of first term), A155934.

Formula

a(n) = A003509(n + 1) - 1. - Sean A. Irvine, Jun 04 2015

Extensions

Edited by Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008