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A005991 Let k(n) denote the least integer such that every n X n (0,1)-matrix with exactly k(n) 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 k(n).
(Formerly M1582)
+0
1
2, 6, 12, 20, 30, 43 (list; graph; listen)
OFFSET

1,1

COMMENT

1 is not in the sequence because a 1 X 1 matrix does not contain a 2 X 2 submatrix. - Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 02 2008

REFERENCES

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

Problem E2429, Amer. Math. Monthly, 81 (1974), 1112-1113.

LINKS

Index entries for sequences related to binary matrices

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

Sequence in context: A160929 A103505 A002378 this_sequence A003274 A121315 A078878

Adjacent sequences: A005988 A005989 A005990 this_sequence A005992 A005993 A005994

KEYWORD

nonn,more

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

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

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Last modified November 27 14:50 EST 2009. Contains 167570 sequences.


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