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

1,2

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

Links

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

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

Example

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

Crossrefs

Column 1 is A007582(n-1)

Column 2 is A199560(n-1)

Row 1 is A007051(n-1)

Sequence in context: A370850 A126333 A266192 * A039575 A291923 A283448

Adjacent sequences: A233079 A233080 A233081 * A233083 A233084 A233085

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 03 2013

Status

approved