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A235884 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2X2 subblock 9
21, 51, 51, 129, 105, 129, 339, 231, 231, 339, 921, 537, 453, 537, 921, 2571, 1311, 951, 951, 1311, 2571, 7329, 3345, 2109, 1833, 2109, 3345, 7329, 21219, 8871, 4911, 3759, 3759, 4911, 8871, 21219, 62121, 24297, 11973, 8097, 7221, 8097, 11973, 24297, 62121 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Table starts

.....21.....51....129....339....921...2571...7329...21219...62121..183291

.....51....105....231....537...1311...3345...8871...24297...68271..195585

....129....231....453....951...2109...4911..11973...30471...80589..220191

....339....537....951...1833...3759...8097..18231...42873..105279..269457

....921...1311...2109...3759...7221..14631..30909...67839..154821..368151

...2571...3345...4911...8097..14631..28185..56751..118257..254391..566025

...7329...8871..11973..18231..30909..56751.109893..220551..454989..963231

..21219..24297..30471..42873..67839.118257.220551..429513..860559.1762017

..62121..68271..80589.105279.154821.254391.454989..860559.1684821.3372711

.183291.195585.220191.269457.368151.566025.963231.1762017.3372711.6633465

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..390

FORMULA

Empirical for diagonal and column k (the k=2 recurrence also works for k=1; apparently all rows and columns satisfy the same order 3 recurrence):

diagonal: a(n) = 10*a(n-1) -35*a(n-2) +50*a(n-3) -24*a(n-4)

k=1: a(n) = 5*a(n-1) -6*a(n-2)

k=2..7..(?): a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3)

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..0..0....2..1..1..2..2....2..2..2..2..1....1..1..0..1..1

..0..0..0..0..0....1..2..2..1..1....2..2..2..2..1....1..1..0..1..1

..2..2..2..2..2....1..2..2..1..1....1..1..1..1..2....1..1..0..1..1

..2..2..2..2..2....1..2..2..1..1....1..1..1..1..2....0..0..1..0..0

..1..1..1..1..1....1..2..2..1..1....2..2..2..2..1....1..1..0..1..1

..1..1..1..1..1....1..2..2..1..1....2..2..2..2..1....0..0..1..0..0

CROSSREFS

Sequence in context: A147281 A130062 A153441 * A053178 A166150 A224334

Adjacent sequences:  A235881 A235882 A235883 * A235885 A235886 A235887

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jan 16 2014

STATUS

approved

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Last modified October 17 21:17 EDT 2021. Contains 348065 sequences. (Running on oeis4.)