A236997 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with the maximum plus the lower median minus the upper median minus the minimum of every 2X2 subblock differing from its horizontal and vertical neighbors by exactly one

81, 360, 360, 1600, 2376, 1600, 7200, 15552, 15552, 7200, 32400, 104976, 149632, 104976, 32400, 144000, 699840, 1513728, 1513728, 699840, 144000, 640000, 4618944, 14963200, 23825664, 14963200, 4618944, 640000, 2880000, 30233088, 145732608

Offset

1,1

Comments

Table starts

.......81........360..........1600............7200.............32400

......360.......2376.........15552..........104976............699840

.....1600......15552........149632.........1513728..........14963200

.....7200.....104976.......1513728........23825664.........363916800

....32400.....699840......14963200.......363916800........8552563200

...144000....4618944.....145732608......5454273024......192222720000

...640000...30233088....1406076928.....80675315712.....4279521280000

..2880000..204073344...14212288512...1304215105536...109212364800000

.12960000.1360488960..140607692800..20389194547200..2683631554560000

.57600000.8979227136.1372136620032.312112856088576.62224920576000000

Links

R. H. Hardin, Table of n, a(n) for n = 1..364

Formula

Empirical for column k:

k=1: a(n) = 400*a(n-4)

k=2: a(n) = 1944*a(n-4)

k=3: a(n) = 10*a(n-1) +8704*a(n-4) -87040*a(n-5)

k=4: a(n) = 158112*a(n-4) -7941224448*a(n-8) +124128835928064*a(n-12)

k=5: [order 16]

k=6: [order 17]

k=7: [order 15]

Example

Some solutions for n=3 k=4
..0..0..0..1..0....0..0..0..1..2....0..0..1..1..2....0..0..1..1..0
..2..1..1..1..0....0..2..1..2..0....2..1..0..1..2....2..1..0..1..2
..2..1..0..2..2....0..1..2..0..0....1..0..0..1..1....1..0..2..1..1
..2..0..1..2..2....2..1..1..1..0....0..0..0..0..0....0..2..0..0..2

Crossrefs

Sequence in context: A237723 A237472 A237465 * A236065 A206676 A205520

Adjacent sequences: A236994 A236995 A236996 * A236998 A236999 A237000

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 02 2014

Status

approved