A238726 T(n,k)=Number of nXk 0..2 arrays with no element equal to the sum modulo 3 of elements to its left or elements above it

2, 2, 2, 4, 4, 4, 4, 10, 10, 4, 8, 16, 40, 16, 8, 8, 42, 86, 86, 42, 8, 16, 64, 336, 284, 336, 64, 16, 16, 170, 704, 1506, 1506, 704, 170, 16, 32, 256, 2704, 4636, 11440, 4636, 2704, 256, 32, 32, 682, 5660, 24298, 48538, 48538, 24298, 5660, 682, 32, 64, 1024, 21504, 73300

Offset

1,1

Comments

Table starts

..2....2.....4.......4........8..........8..........16...........16

..2....4....10......16.......42.........64.........170..........256

..4...10....40......86......336........704........2704.........5660

..4...16....86.....284.....1506.......4636.......24298........73300

..8...42...336....1506....11440......48538......359456......1502622

..8...64...704....4636....48538.....296384.....3022230.....17949864

.16..170..2704...24298...359456....3022230....43248968....354823094

.16..256..5660...73300..1502622...17949864...354823094...4105077596

.32..682.21504..381280.10971288..180550234..4990305568..79679547754

.32.1024.45176.1144292.45750856.1061806368.40601871406.909801061032

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-2) -4*a(n-4)

k=3: a(n) = 17*a(n-2) -96*a(n-4) +210*a(n-6) -152*a(n-8)

k=4: [order 18]

k=5: [order 38]

k=6: [order 90]

Example

Some solutions for n=5 k=4
..2..1..1..2....1..2..1..2....1..2..1..2....1..2..2..1....2..1..2..1
..1..0..2..1....2..0..0..1....2..1..2..1....2..1..1..2....1..2..1..0
..1..2..2..1....1..0..2..1....2..1..1..2....2..1..2..1....2..1..1..0
..2..1..1..2....2..1..2..0....1..2..2..0....1..2..1..2....1..0..2..2
..1..2..2..1....2..1..1..0....1..2..2..0....1..2..1..2....2..0..1..2

Crossrefs

Sequence in context: A355911 A369207 A113402 * A240321 A054861 A187324

Adjacent sequences: A238723 A238724 A238725 * A238727 A238728 A238729

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 03 2014

Status

approved