A231451 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 antidiagonal neighbors, with values 0..3 introduced in row major order

2, 3, 6, 4, 15, 23, 7, 32, 97, 102, 12, 87, 340, 715, 492, 24, 229, 1598, 4179, 5643, 2485, 48, 647, 7429, 33659, 54868, 46075, 12858, 103, 1829, 38713, 265510, 738459, 741430, 382341, 67354, 222, 5293, 203544, 2308095, 9796477, 16471575, 10145989, 3196783

Offset

1,1

Comments

Table starts

.......2.........3...........4.............7..............12.................24

.......6........15..........32............87.............229................647

......23........97.........340..........1598............7429..............38713

.....102.......715........4179.........33659..........265510............2308095

.....492......5643.......54868........738459.........9796477..........144109697

....2485.....46075......741430......16471575.......367351650.........9081622778

...12858....382341....10145989.....370059818.....13839802182.......572792301557

...67354...3196783...139597860....8337875579....522071407304.....36148438185936

..355003..26821757..1925134584..188061528227..19702443415959...2281891799253071

.1876862.225400759.26574209688.4243377409271.743668294490912.144055012148018656

Links

R. H. Hardin, Table of n, a(n) for n = 1..126

Formula

Empirical for column k:

k=1: a(n) = 11*a(n-1) -41*a(n-2) +65*a(n-3) -43*a(n-4) +9*a(n-5)

k=2: [order 7]

k=3: [order 17]

k=4: [order 25]

k=5: [order 65]

Empirical for row n:

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

n=2: [order 16]

n=3: [order 50] for n>51

Example

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

Crossrefs

Row 1 is A231337(n-1)

Sequence in context: A227296 A318846 A231263 * A126063 A214352 A248090

Adjacent sequences: A231448 A231449 A231450 * A231452 A231453 A231454

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 09 2013

Status

approved