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A241114 T(n,k)=Number of nXk 0..2 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..2 introduced in row major order 6
1, 2, 2, 5, 14, 5, 14, 113, 113, 14, 41, 953, 2612, 953, 41, 122, 8037, 60340, 60340, 8037, 122, 365, 67774, 1394492, 3829419, 1394492, 67774, 365, 1094, 571530, 32228144, 242964166, 242964166, 32228144, 571530, 1094, 3281, 4819638, 744822776 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Table starts

...1......2.........5...........14...............41.................122

...2.....14.......113..........953.............8037...............67774

...5....113......2612........60340..........1394492............32228144

..14....953.....60340......3829419........242964166.........15415566961

..41...8037...1394492....242964166......42319480270.......7371117761274

.122..67774..32228144..15415566961....7371117761274....3524558549098471

.365.571530.744822776.978087593971.1283885768594047.1685292182142705704

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..112

FORMULA

Empirical for column k:

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

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

k=3: [order 12] for n>13

k=4: [order 42] for n>43

EXAMPLE

Some solutions for n=3 k=4

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

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

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

CROSSREFS

Column 1 is A007051(n-1)

Column 2 is A199649

Sequence in context: A275352 A282056 A199655 * A208392 A282275 A208201

Adjacent sequences:  A241111 A241112 A241113 * A241115 A241116 A241117

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Apr 16 2014

STATUS

approved

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Last modified April 19 20:04 EDT 2019. Contains 322291 sequences. (Running on oeis4.)