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 A178994 T(n,k) = Maximum number Q for an n X k 1..Q array with each value in 1..Q horizontally or vertically adjacent to each other value at least once, or -1 if no such number exists. 1
 1, 2, 2, 2, 3, 2, 3, 4, 4, 3, 3, 4, 5, 4, 3, 3, 5, 6, 6, 5, 3, 3, 6, 6, 7, 6, 6, 3, 4, 6, 7, 8, 8, 7, 6, 4, 4, 7, 8, 8, 9, 8, 8, 7, 4, 4, 7, 8, 9, 10, 10, 9, 8, 7, 4, 5, 7, 9, 10, 11, 11, 11, 10, 9, 7, 5, 5, 7, 10, 11, 12, 12, 12, 12, 11, 10, 7, 5, 5, 8, 10, 11, 12, 12, 13, 12, 12, 11, 10, 8, 5, 5, 8, 11 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Table starts .1..2..2..3..3..3..3..4..4..4..5..5..5..5..5..5..5..6..6.6 .2..3..4..4..5..6..6..7..7..7..7..8..8..9..9.10.10.10.10 .2..4..5..6..6..7..8..8..9.10.10.11.11.-1.12.12.13.13 .3..4..6..7..8..8..9.10.11.11.12.13.13.14.14.15.15 .3..5..6..8..9.10.11.12.12.13.-1.14.15.16.16.-1 .3..6..7..8.10.11.12.12.-1.14.15.16.-1.17.-1 .3..6..8..9.11.12.13.14.15.16.-1.17.18.-1 .4..7..8.10.12.12.14.15.16.-1.-1.-1.19 .4..7..9.11.12.-1.15.16.17.-1.19.-1 .4..7.10.11.13.14.16.-1.-1.19.-1 .5..7.10.12.-1.15.-1.-1.19.-1 .5..8.11.13.14.16.17.-1.-1 .5..8.11.13.15.-1.18.19 .5..9.-1.14.16.17.-1 .5..9.12.14.16.-1 .5.10.12.15.-1 .5.10.13.15 .6.10.13 .6.10 .6 LINKS R. H. Hardin, Table of n, a(n) for n = 1..210 (T read by antidiagonals) FORMULA T(n,k) <= floor((1+sqrt(16kn-8k-8n+1))/2) but empirically either 0 or 1 below this maximum EXAMPLE n X n solutions with a maximal Q=2n-1 ..1..2..3..4..5.....1..2..3..4.....1..2..3.....1..2.....1 ..6..7..8..9..1.....5..6..7..1.....4..5..1.....3..2 ..2..3..4..6..3.....2..4..5..3.....2..3..4 ..5..9..2..8..5.....7..7..1..6 ..6..7..4..1..7 ... .15.14.13.15.12.14.11.15...1..2..3..4..5..6..7.....1..2..3..4..5..6 .10..9.12..8.11.10.13..9...8..9.10.11.12.13..1.....7..8..9.10.11..1 .12..7..6.14..7..8..6.11...2..3..4..5..6..7.11.....2..3..4..6..7..3 ..5.15..4..5.13..4.10..5...4..1..6..2.10.12..2.....5..3.11..8..5.10 ..9..6..3..8..2.14..3..7...9.12..3.13..8..4..7.....9..6..2..4..1..8 ..8..1.15.13..3..1.12..4...6..8..7.10..5.13..9.....1.11..9..7.10..2 .15.11..2..1..9..4..2.11..11..3..5..1..9.11..8 ..5..1.10..7..2..6..5..3 ... ..1..2..3..1..4..2..5..1..6..2.....1..2..3..1..4..2..5..1..6 ..7..8..4..9..5..7..3..8..5.10.....7..6..4..8..5..7..3..9..5 ..4..6.10..3.11..6.12..9.13..1.....4..9.10..2.11..8..6.11.10 .11..9..7.13..2.14..1.15..4.16....11..7.12..9.13..3.10..1.13 ..1.17.11..8.12..4.18..2.17..3.....3.14..1.15..2.12..8.16..4 .19..5.12.10.13.19..3..6.13.14....15..4.17..5.14..6.13..7.10 ..2.16..7.14.11.10.15.16.18..5....11.12.13.16..9.17.14.15.15 ..9.10.17..8.15.18..6.17.12.15.....2.17.10.14..8.15.12.16..6 .14.12.19.16.13..7.19.14.16..7....16..3.16.11.17.13..5.17..7 .15.17.18..9.19.15..8.18.11.19 CROSSREFS Sequence in context: A068324 A167505 A165015 * A306608 A143976 A194296 Adjacent sequences:  A178991 A178992 A178993 * A178995 A178996 A178997 KEYWORD sign,tabl AUTHOR R. H. Hardin, Jan 03 2011 EXTENSIONS Definition extended by Georg Fischer, Feb 15 2019 STATUS approved

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Last modified October 16 18:38 EDT 2019. Contains 328102 sequences. (Running on oeis4.)