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A070259 Array f(m,n) read by antidiagonals: f(m,n) = minimal number of 0's in a 2m X 2n (0,1) matrix that contains no m X n submatrix of 1's (m >= 1, n >= 1). 1

%I #4 Mar 30 2012 16:49:19

%S 4,6,6,8,7,8,10,9,9,10,12,11,10,11,12,14,13,13,13,13,14,16,15,14,13,

%T 14,15,16,18,17,16,16,16,16,17,18,20,19,18,18,16,18,18,19,20,22,21,20,

%U 19,20,20,19,20,21,22,24,23,22,21,22,19,22,21,22,23,24,26,25,24,24,24,23

%N Array f(m,n) read by antidiagonals: f(m,n) = minimal number of 0's in a 2m X 2n (0,1) matrix that contains no m X n submatrix of 1's (m >= 1, n >= 1).

%D J. R. Griggs and C.-C. Ho, On the half-case of the Zarankiewicz problem, Discrete Math., 249 (2002), 95-104.

%e Comment from Hermann Jamke: Array begins:

%e 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, ...

%e 6, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, ...

%e 8, 9, 10, 13, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, ...

%e 10, 11, 13, 13, 16, 18, 19, 21, 24, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, ...

%e 12, 13, 14, 16, 16, 20, 22, 24, 24, 26, 29, 32, 32, 34, 36, 39, 40, 42, 44, 46, ...

%e 14, 15, 16, 18, 20, 19, 23, 25, 27, 29, 29, 31, 34, 37, 39, 39, 41, 43, 46, 49, ...

%e 16, 17, 18, 19, 22, 23, 22, 26, 29, 31, 33, 34, 34, 36, 40, 42, 45, 47, 46, 48, ...

%e 18, 19, 20, 21, 24, 25, 26, ...

%e 20, 21, 22, 24, 24, 27, 29, ...

%e 22, 23, 24, 25, 26, 29, 31, ...

%e 24, 25, 26, 27, 29, 29, 33, ...

%e 26, 27, 28, 29, 32, 31, 34, ...

%e 28, 29, 30, 31, 32, 34, 34, ...

%e 30, 31, 32, 33, 34, 37, 36, ...

%e 32, 33, 34, 35, 36, 39, 40, ...

%e 34, 35, 36, 37, 39, 39, 42, ...

%e 36, 37, 38, 39, 40, 41, 45, ...

%e 38, 39, 40, 41, 42, 43, 47, ...

%e 40, 41, 42, 43, 44, 46, 46, ...

%e 42, 43, 44, 45, 46, 49, 48, ...

%Y Cf. A070300.

%K nonn,tabl

%O 1,1

%A _N. J. A. Sloane_, May 15 2002

%E Reference gives first 7 rows of the array.

%E More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008

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Last modified June 20 05:29 EDT 2024. Contains 373512 sequences. (Running on oeis4.)