A233082 T(n,k)=Number of nXk 0..3 arrays with no element x(i,j) adjacent to value 3-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 in row major order.

1, 2, 3, 5, 14, 10, 14, 95, 122, 36, 41, 662, 1985, 1094, 136, 122, 4631, 32414, 41675, 9842, 528, 365, 32414, 529862, 1588262, 875165, 88574, 2080, 1094, 226895, 8662343, 60632429, 77824814, 18378455, 797162, 8256, 3281, 1588262, 141615905

Offset: 1

Author

R. H. Hardin, Dec 03 2013

Keywords

• nonn
• tabl

Comments

Table starts

......1.........2.............5................14....................41

......3........14............95...............662..................4631

.....10.......122..........1985.............32414................529862

.....36......1094.........41675...........1588262..............60632429

....136......9842........875165..........77824814............6938214854

....528.....88574......18378455........3813415862..........793945203881

...2080....797162.....385947545......186857377214........90851753687090

...8256...7174454....8104898435.....9156011483462.....10396235291448605

..32896..64570082..170202867125...448644562689614...1189649113515482414

.131328.581130734.3574260209615.21983583571791062.136132453105625552657

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..241

Crossrefs

Column 1 is A007582(n-1)

Column 2 is A199560(n-1)

Row 1 is A007051(n-1)

Formula

Empirical for column k:

k=1: a(n) = 6*a(n-1) -8*a(n-2)

k=2: a(n) = 10*a(n-1) -9*a(n-2)

k=3: a(n) = 22*a(n-1) -21*a(n-2)

k=4: a(n) = 50*a(n-1) -49*a(n-2)

k=5: a(n) = 118*a(n-1) -411*a(n-2) +294*a(n-3)

k=6: a(n) = 283*a(n-1) -4251*a(n-2) +13573*a(n-3) -9604*a(n-4)

k=7: [order 6]

Empirical for row n:

n=1: a(n) = 4*a(n-1) -3*a(n-2)

n=2: a(n) = 8*a(n-1) -7*a(n-2) for n>3

n=3: a(n) = 19*a(n-1) -45*a(n-2) +27*a(n-3) for n>5

n=4: a(n) = 49*a(n-1) -450*a(n-2) +1466*a(n-3) -1853*a(n-4) +789*a(n-5) for n>8

n=5: [order 10] for n>14

n=6: [order 21] for n>26

n=7: [order 52] for n>58