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A232065 T(n,k)=Number of nXk 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal 8
1, 2, 2, 4, 6, 4, 6, 14, 14, 6, 10, 30, 46, 30, 10, 16, 66, 130, 130, 66, 16, 26, 146, 410, 534, 410, 146, 26, 42, 322, 1194, 2230, 2230, 1194, 322, 42, 68, 710, 3722, 9310, 13538, 9310, 3722, 710, 68, 110, 1566, 10942, 38870, 75462, 75462, 38870, 10942, 1566, 110 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1....2......4.......6.......10.........16..........26............42

...2....6.....14......30.......66........146.........322...........710

...4...14.....46.....130......410.......1194........3722.........10942

...6...30....130.....534.....2230.......9310.......38870........162278

..10...66....410....2230....13538......75462......457234.......2561258

..16..146...1194....9310....75462.....612364.....4990482......40661766

..26..322...3722...38870...457234....4990482....59448262.....653375842

..42..710..10942..162278..2561258...40661766...653375842...10508498862

..68.1566..33806..677510.15454594..331554282..7789998594..169516703810

.110.3454.100142.2828606.86936482.2703411654.85859588738.2735194512174

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..312

FORMULA

Empirical for column k:

k=1: a(n) = a(n-1) +a(n-2) for n>3

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

k=3: a(n) = a(n-1) +7*a(n-2) -3*a(n-3) +3*a(n-4) -7*a(n-5) +2*a(n-6) -2*a(n-7) +2*a(n-8)

k=4: a(n) = 4*a(n-1) +a(n-2) -4*a(n-4) -3*a(n-5) +a(n-7) +3*a(n-8) -a(n-11)

k=5: [order 20] for n>22

k=6: [order 42]

EXAMPLE

Some solutions for n=5 k=4

..2..1..0..1....2..1..2..1....2..0..1..0....2..1..2..1....1..2..1..2

..1..0..1..2....1..2..1..2....0..1..2..1....1..0..1..2....0..1..0..1

..0..1..0..1....2..1..2..1....1..0..1..2....0..1..2..1....1..0..1..2

..1..2..1..2....1..0..1..0....2..1..2..1....1..0..1..2....2..1..2..1

..2..1..2..1....2..1..2..1....1..0..1..0....2..1..2..1....1..0..1..0

CROSSREFS

Column 1 is A006355(n+1)

Sequence in context: A166362 A050469 A085730 * A219741 A210603 A252820

Adjacent sequences:  A232062 A232063 A232064 * A232066 A232067 A232068

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Nov 17 2013

STATUS

approved

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Last modified May 16 08:07 EDT 2021. Contains 343940 sequences. (Running on oeis4.)