A240347 T(n,k)=Number of nXk 0..3 arrays with no element equal to one plus the sum of elements to its left or one plus the sum of the elements above it or three plus the sum of the elements diagonally to its northwest, modulo 4

2, 4, 4, 8, 18, 8, 16, 78, 78, 16, 32, 334, 722, 334, 32, 64, 1418, 6376, 6376, 1418, 64, 128, 6002, 55680, 115194, 55680, 6002, 128, 256, 25374, 483926, 2044806, 2044806, 483926, 25374, 256, 512, 107230, 4195892, 36002110, 73440130, 36002110, 4195892

Offset

1,1

Comments

Table starts

....2.......4..........8............16..............32..............64

....4......18.........78...........334............1418............6002

....8......78........722..........6376...........55680..........483926

...16.....334.......6376........115194.........2044806........36002110

...32....1418......55680.......2044806........73440130......2607237326

...64....6002.....483926......36002110......2607237326....186214281670

..128...25374....4195892.....631121148.....92003133794..13200773101956

..256..107230...36331704...11038084086...3236101836296.932020621734728

..512..453098..314419494..192823850946.113624636162418

.1024.1914498.2720368268.3366365227614

Links

R. H. Hardin, Table of n, a(n) for n = 1..97

Formula

Empirical for column k:

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

k=2: a(n) = 6*a(n-1) -7*a(n-2) -4*a(n-3) +8*a(n-4)

k=3: [order 23]

Example

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

Crossrefs

Column 1 is A000079

Sequence in context: A291778 A089887 A161816 * A160124 A295293 A080007

Adjacent sequences: A240344 A240345 A240346 * A240348 A240349 A240350

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 04 2014

Status

approved