A231343 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element unequal to a strict majority of its horizontal and vertical neighbors, with values 0..3 introduced in row major order

3, 4, 4, 7, 9, 7, 12, 22, 22, 12, 24, 59, 96, 59, 24, 48, 159, 453, 453, 159, 48, 103, 439, 2302, 3572, 2302, 439, 103, 222, 1236, 12052, 30269, 30269, 12052, 1236, 222, 493, 3527, 65326, 259011, 465033, 259011, 65326, 3527, 493, 1100, 10184, 358429

Offset

1,1

Comments

Table starts

....3.....4........7........12.........24.........48........103..........222

....4.....9.......22........59........159........439.......1236.........3527

....7....22.......96.......453.......2302......12052......65326.......358429

...12....59......453......3572......30269.....259011....2278003.....20081717

...24...159.....2302.....30269.....465033....6871838..105988195...1613424264

...48...439....12052....259011....6871838..169968099.4400551358.111907856129

..103..1236....65326...2278003..105988195.4400551358

..222..3527...358429..20081717.1613424264

..493.10184..1989453.178468093

.1100.29679.11087559

Links

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

Formula

Empirical for column k:

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

k=2: a(n) = 5*a(n-1) -6*a(n-2) +2*a(n-3) -8*a(n-4) +6*a(n-5) -a(n-6) +3*a(n-7)

k=3: [order 34]

k=4: [order 97] for n>98

Example

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

Crossrefs

Sequence in context: A014406 A154426 A231219 * A121924 A241740 A342332

Adjacent sequences: A231340 A231341 A231342 * A231344 A231345 A231346

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 07 2013

Status

approved