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). (Formerly M1582)

2, 6, 12, 20, 30, 43

Offset

1,1

References

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

Links

Table of n, a(n) for n=1..6.

E. T. Wang and R. K. Guy, Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113.

Index entries for sequences related to binary matrices

Formula

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

Example

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

Crossrefs

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

Sequence in context: A279019 A002378 A349704 * A266194 A194110 A291876

Adjacent sequences: A005988 A005989 A005990 * A005992 A005993 A005994

Keyword

nonn,more

Author

N. J. A. Sloane

Extensions

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

Status

approved