A233239 T(n,k)=Number of nXk 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally, diagonally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

1, 2, 3, 6, 19, 11, 23, 271, 313, 48, 99, 4504, 18744, 6046, 236, 452, 79201, 1212549, 1409129, 123352, 1248, 2136, 1419889, 79794804, 338046654, 107709266, 2565169, 6896, 10313, 25622596, 5267525102, 81477098771, 94601758339, 8259321811

Offset: 1

Author

R. H. Hardin, Dec 06 2013

Keywords

• nonn
• tabl

Comments

Table starts

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

.......3...........19................271.....................4504

......11..........313..............18744..................1212549

......48.........6046............1409129................338046654

.....236.......123352..........107709266..............94601758339

....1248......2565169.........8259321811...........26484848685044

....6896.....53692063.......633724470764.........7415057313896849

...39168...1126297996.....48630297616989......2076029517168733114

..226496..23643610702...3731839458899046....581236325493128357679

.1325568.496455294319.286378755661153351.162731637919752077883024

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..127

Crossrefs

Column 1 is A233162(n+1)

Column 2 is A233107

Row 1 is A233106

Formula

Empirical for column k:

k=1: a(n) = 12*a(n-1) -44*a(n-2) +48*a(n-3)

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

k=3: a(n) = 93*a(n-1) -1273*a(n-2) +1943*a(n-3) -882*a(n-4) +120*a(n-5)

k=4: a(n) = 311*a(n-1) -8722*a(n-2) +10022*a(n-3) -1645*a(n-4) +35*a(n-5)

Empirical for row n:

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

n=2: a(n) = 23*a(n-1) -81*a(n-2) -143*a(n-3) +82*a(n-4) +120*a(n-5) for n>6

n=3: [order 9] for n>10

n=4: [order 21] for n>22