A233113 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or vertically, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

1, 2, 2, 6, 19, 6, 23, 313, 313, 23, 99, 6046, 24912, 6046, 99, 452, 123352, 2154065, 2154065, 123352, 452, 2136, 2565169, 189286871, 794723482, 189286871, 2565169, 2136, 10313, 53692063, 16683923848, 294285758398, 294285758398, 16683923848

Offset: 1

Author

R. H. Hardin, Dec 04 2013

Keywords

• nonn
• tabl

Comments

Table starts

....1........2.............6................23.....................99

....2.......19...........313..............6046.................123352

....6......313.........24912...........2154065..............189286871

...23.....6046.......2154065.........794723482...........294285758398

...99...123352.....189286871......294285758398........457873555330159

..452..2565169...16683923848...109015274761891.....712427482567592092

.2136.53692063.1471365099497.40385221182281560.1108502928092713640626

Examples

			Some solutions for n=3 k=4
..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..0
..0..2..2..5....1..1..0..2....1..0..4..2....2..4..2..5....0..0..1..0
..0..2..1..2....2..1..1..5....0..1..3..1....4..0..0..3....2..2..0..1
		

Links

• R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 9*a(n-1) -23*a(n-2) +15*a(n-3)

k=2: a(n) = 29*a(n-1) -175*a(n-2) +147*a(n-3)

k=3: a(n) = 111*a(n-1) -2128*a(n-2) +10532*a(n-3) -17559*a(n-4) +9045*a(n-5)

k=4: [order 7]

k=5: [order 15]