A200795 -id:A200795 - cp's OEIS frontend

A200801 T(n,k) is the number of n X k 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

1, 2, 2, 5, 15, 5, 15, 178, 178, 15, 51, 2614, 9880, 2614, 51, 187, 40148, 583813, 583813, 40148, 187, 715, 622645, 34679839, 132636590, 34679839, 622645, 715, 2795, 9676364, 2060918000, 30147154218, 30147154218, 2060918000, 9676364, 2795

Offset: 1

R. H. Hardin, Nov 22 2011

			Table starts:
.....1...........2.................5......................15
.....2..........15...............178....................2614
.....5.........178..............9880..................583813
....15........2614............583813...............132636590
....51.......40148..........34679839.............30147154218
...187......622645........2060918000...........6852264918471
...715.....9676364......122478253815........1557479347400065
..2795...150442627.....7278777317468......354005859128023982
.11051..2339207390...432571571252989....80463441477635545163
.43947.36372631268.25707362563355693.18288865135614195620421
...
Some solutions for n=5 and k=3:
..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
..0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0....0..1..0
..2..0..0....0..1..1....0..0..2....2..2..0....2..2..0....2..2..0....2..1..2
..2..3..3....1..0..2....3..1..0....1..1..1....3..2..2....0..0..1....0..1..3
..2..2..0....3..2..1....3..3..0....2..2..1....3..1..3....1..1..1....1..1..2

Ron Hardin, Table of n, a(n) for n = 1..97

Main diagonal is A200794.
Columns 1..7 are A007581(n-1), A200795, A200796, A200797, A200798, A200799, A200780.
Cf. A199655, A198528.

A241119 T(n,k)=Number of nXk 0..3 arrays with no element equal to exactly three horizontal or vertical neighbors, with new values 0..3 introduced in row major order.

Original entry on oeis.org

1, 2, 2, 5, 15, 5, 15, 178, 178, 15, 51, 2614, 9918, 2614, 51, 187, 40148, 587555, 587555, 40148, 187, 715, 622645, 35000157, 134229632, 35000157, 622645, 715, 2795, 9676364, 2085879115, 30679522712, 30679522712, 2085879115, 9676364, 2795

Offset: 1

R. H. Hardin, Apr 16 2014

Table starts
...1......2..........5............15................51..................187
...2.....15........178..........2614.............40148...............622645
...5....178.......9918........587555..........35000157...........2085879115
..15...2614.....587555.....134229632.......30679522712........7012241396116
..51..40148...35000157...30679522712....26891788727245....23571710809729613
.187.622645.2085879115.7012241396116.23571710809729613.79236581561126536192

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

R. H. Hardin, Table of n, a(n) for n = 1..84

Column 1 is A007581(n-1)

Column 2 is A200795

Empirical for column k:
k=1: a(n) = 7*a(n-1) -14*a(n-2) +8*a(n-3)
k=2: [order 8] for n>10
k=3: [order 20] for n>21
k=4: [order 74] for n>75

cp's OEIS Frontend

A200801 T(n,k) is the number of n X k 0..3 arrays with values 0..3 introduced in row major order and each element equal to no more than two horizontal and vertical neighbors.

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