A235962 T(n,k)=Number of (n+1)X(k+1) 0..1 arrays with the difference of the upper and lower median value of each 2X2 subblock in lexicographically nondecreasing order columnwise and nonincreasing rowwise

16, 50, 50, 144, 228, 144, 398, 928, 928, 398, 1076, 3574, 5196, 3574, 1076, 2866, 13346, 27296, 27296, 13346, 2866, 7560, 48848, 137988, 195428, 137988, 48848, 7560, 19798, 176420, 681546, 1340034, 1340034, 681546, 176420, 19798, 51580, 631130

Offset

1,1

Comments

Table starts

.....16......50.......144.........398.........1076...........2866

.....50.....228.......928........3574........13346..........48848

....144.....928......5196.......27296.......137988.........681546

....398....3574.....27296......195428......1340034........8974124

...1076...13346....137988.....1340034.....12412248......112308598

...2866...48848....681546.....8974124....112308598.....1374773712

...7560..176420...3311312....59037352....997114552....16500794898

..19798..631130..15908352...383935642...8749889970...195824119834

..51580.2242678..75789960..2474858156..76070757246..2302059880080

.133850.7930164.358924192.15855538026.657191443192.26894984140858

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) -a(n-2) -10*a(n-3) +8*a(n-4)

k=2: [order 8]

k=3: [order 17]

k=4: [order 32]

k=5: [order 67]

Example

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

Crossrefs

Column 1 is A235566

Sequence in context: A153483 A030686 A030688 * A235573 A186850 A235566

Adjacent sequences: A235959 A235960 A235961 * A235963 A235964 A235965

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 17 2014

Status

approved