A251210 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with every 2X2 subblock summing to a nonzero multiple of 2

40, 180, 180, 816, 1246, 816, 3728, 8870, 8870, 3728, 17152, 65040, 102811, 65040, 17152, 79424, 489772, 1273440, 1273440, 489772, 79424, 369920, 3775022, 16687766, 27920380, 16687766, 3775022, 369920, 1731840, 29664576, 228610911, 667858580

Offset

1,1

Comments

Table starts

.......40.........180............816.............3728...............17152

......180........1246...........8870............65040..............489772

......816........8870.........102811..........1273440............16687766

.....3728.......65040........1273440.........27920380...........667858580

....17152......489772.......16687766........667858580.........29868134632

....79424.....3775022......228610911......16965787428.......1430667235078

...369920....29664576.....3233921644.....447556857260......71260903869938

..1731840...236740252....46763019686...12076357468990....3627694408668076

..8144896..1912108322...686058347195..330184315214356..186917463235694336

.38458368.15584536740.10159339091240.9097022461368016.9695744269718563214

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

Formula

Empirical for column k:

k=1: a(n) = 8*a(n-1) -12*a(n-2) -16*a(n-3)

k=2: a(n) = 18*a(n-1) -90*a(n-2) +7*a(n-3) +576*a(n-4) +210*a(n-5) -180*a(n-6)

k=3: [order 14]

k=4: [order 30]

k=5: [order 65]

Example

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

Crossrefs

Sequence in context: A322774 A264547 A327430 * A211497 A251203 A187510

Adjacent sequences: A251207 A251208 A251209 * A251211 A251212 A251213

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 30 2014

Status

approved