A239155 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order

1, 2, 1, 7, 2, 7, 24, 7, 55, 17, 88, 24, 868, 208, 96, 328, 88, 12159, 5775, 2778, 340, 1235, 328, 175471, 135766, 209839, 17050, 1639, 4668, 1235, 2519488, 3313304, 12844591, 2709568, 166531, 6623, 17675, 4668, 36221263, 80240064, 821135900, 330311070

Offset

1,2

Comments

Table starts

....1.......2..........7...........24..............88................328

....1.......2..........7...........24..............88................328

....7......55........868........12159..........175471............2519488

...17.....208.......5775.......135766.........3313304...........80240064

...96....2778.....209839.....12844591.......821135900........52019283568

..340...17050....2709568....330311070.....42600989632......5427557363908

.1639..166531...63961519..18120156500...5469574400477...1628795409782566

.6623.1221727.1049404191.629468400383.407538214264758.259498303698165490

Links

R. H. Hardin, Table of n, a(n) for n = 1..113

Formula

Empirical for column k:

k=1: a(n) = 4*a(n-1) +7*a(n-2) -26*a(n-3) +5*a(n-4) +14*a(n-5)

k=2: [order 14]

k=3: [order 9]

Empirical for row n:

n=1: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)

n=2: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)

n=3: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6)

n=4: [order 14]

n=5: [order 57]

Example

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

Crossrefs

Row 1 and 2 are A221454(n+1)

Sequence in context: A213053 A200236 A292191 * A097411 A134929 A160413

Adjacent sequences: A239152 A239153 A239154 * A239156 A239157 A239158

Keyword

nonn,tabl

Author

R. H. Hardin, Mar 11 2014

Status

approved