A070259 - OEIS

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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).

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, 14, 15, 16, 18, 17, 16, 16, 16, 16, 17, 18, 20, 19, 18, 18, 16, 18, 18, 19, 20, 22, 21, 20, 19, 20, 20, 19, 20, 21, 22, 24, 23, 22, 21, 22, 19, 22, 21, 22, 23, 24, 26, 25, 24, 24, 24, 23 (list; table; graph; refs; listen; history; internal format)

	OFFSET	`1,1`
	REFERENCES	`J. R. Griggs and C.-C. Ho, On the half-case of the Zarankiewicz problem, Discrete Math., 249 (2002), 95-104.`
	EXAMPLE	`Comment from Hermann Jamke: Array begins:` `4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, ...` `6, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, ...` `8, 9, 10, 13, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, ...` `10, 11, 13, 13, 16, 18, 19, 21, 24, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, ...` `12, 13, 14, 16, 16, 20, 22, 24, 24, 26, 29, 32, 32, 34, 36, 39, 40, 42, 44, 46, ...` `14, 15, 16, 18, 20, 19, 23, 25, 27, 29, 29, 31, 34, 37, 39, 39, 41, 43, 46, 49, ...` `16, 17, 18, 19, 22, 23, 22, 26, 29, 31, 33, 34, 34, 36, 40, 42, 45, 47, 46, 48, ...` `18, 19, 20, 21, 24, 25, 26, ...` `20, 21, 22, 24, 24, 27, 29, ...` `22, 23, 24, 25, 26, 29, 31, ...` `24, 25, 26, 27, 29, 29, 33, ...` `26, 27, 28, 29, 32, 31, 34, ...` `28, 29, 30, 31, 32, 34, 34, ...` `30, 31, 32, 33, 34, 37, 36, ...` `32, 33, 34, 35, 36, 39, 40, ...` `34, 35, 36, 37, 39, 39, 42, ...` `36, 37, 38, 39, 40, 41, 45, ...` `38, 39, 40, 41, 42, 43, 47, ...` `40, 41, 42, 43, 44, 46, 46, ...` `42, 43, 44, 45, 46, 49, 48, ...`
	CROSSREFS	`Cf. A070300.` `Sequence in context: A103411 A200118 A074672 * A111653 A173395 A049089` `Adjacent sequences: A070256 A070257 A070258 * A070260 A070261 A070262`
	KEYWORD	`nonn,tabl`
	AUTHOR	`N. J. A. Sloane (njas(AT)research.att.com), May 15 2002`
	EXTENSIONS	`Reference gives first 7 rows of the array.` `More terms from Herman Jamke (hermanjamke(AT)fastmail.fm), Mar 30 2008`

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Last modified February 15 09:00 EST 2012. Contains 205746 sequences.