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

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

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