A232137 T(n,k)=Number of (n+1)X(k+1) 0..2 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with values 0..2 introduced in row major order

6, 36, 44, 200, 728, 328, 1140, 10956, 14752, 2448, 6468, 169692, 602468, 298912, 18272, 36752, 2616952, 25364480, 33162868, 6056640, 136384, 208772, 40399768, 1063744484, 3795674252, 1825568436, 122721280, 1017984, 1186044, 623543776

Offset

1,1

Comments

Table starts

.....6......36........200.........1140............6468.............36752

....44.....728......10956.......169692.........2616952..........40399768

...328...14752.....602468.....25364480......1063744484.......44671124016

..2448..298912...33162868...3795674252....433383414596....49550984711452

.18272.6056640.1825568436.568008109436.176569302110496.54960219182423136

Links

R. H. Hardin, Table of n, a(n) for n = 1..143

Formula

Empirical for column k:

k=1: a(n) = 8*a(n-1) -4*a(n-2)

k=2: a(n) = 22*a(n-1) -36*a(n-2) +16*a(n-3)

k=3: [order 8]

k=4: [order 14]

k=5: [order 34] for n>36

Empirical for row n:

n=1: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4)

n=2: [order 17]

n=3: [order 76] for n>77

Example

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

Crossrefs

Column 1 is A102591

Sequence in context: A043063 A348384 A328466 * A008460 A132633 A372945

Adjacent sequences: A232134 A232135 A232136 * A232138 A232139 A232140

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 19 2013

Status

approved