login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

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