A230184 T(n,k)=Number of nXk 0..2 arrays x(i,j) with each element horizontally or antidiagonally next to at least one element with value 2-x(i,j)

0, 3, 0, 3, 9, 0, 9, 27, 33, 0, 15, 159, 231, 129, 0, 33, 825, 3411, 1971, 513, 0, 63, 4395, 44487, 73857, 16815, 2049, 0, 129, 23307, 596973, 2432241, 1603431, 143451, 8193, 0, 255, 123729, 7957785, 82359177, 133265847, 34825803, 1223799, 32769, 0, 513

Offset

1,2

Comments

Table starts

.0.....3........3...........9.............15................33

.0.....9.......27.........159............825..............4395

.0....33......231........3411..........44487............596973

.0...129.....1971.......73857........2432241..........82359177

.0...513....16815.....1603431......133265847.......11393567289

.0..2049...143451....34825803.....7303192425.....1576417829097

.0..8193..1223799...756450105...400233701367...218117038953009

.0.32769.10440387.16430979183.21933865129257.30179260908320577

Links

R. H. Hardin, Table of n, a(n) for n = 1..238

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) -4*a(n-2)

k=3: a(n) = 9*a(n-1) -4*a(n-2)

k=4: a(n) = 26*a(n-1) -97*a(n-2) +89*a(n-3) -18*a(n-4) +a(n-5)

k=5: [order 6] for n>8

k=6: [order 23] for n>24

k=7: [order 34] for n>37

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) +7*a(n-2) +a(n-3) -6*a(n-4) -5*a(n-5) for n>6

n=3: [order 21] for n>23

n=4: [order 93] for n>96

Example

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

Crossrefs

Column 2 is A084508(n+1)

Row 1 is A062510(n-1)

Sequence in context: A117940 A099093 A137339 * A132330 A117078 A021333

Adjacent sequences: A230181 A230182 A230183 * A230185 A230186 A230187

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 11 2013

Status

approved