A199649 -id:A199649 - cp's OEIS frontend

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

R. H. Hardin, Apr 16 2014

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

			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

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

Column 1 is A007051(n-1)

Column 2 is A199649

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

cp's OEIS Frontend

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.

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