A231227 T(n,k)=Number of (n+2)X(k+2) 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical, diagonal and antidiagonal neighbors, with values 0..2 introduced in row major order

1, 2, 2, 3, 4, 3, 6, 8, 8, 6, 11, 17, 21, 17, 11, 22, 45, 54, 54, 45, 22, 43, 103, 185, 182, 185, 103, 43, 86, 264, 552, 812, 812, 552, 264, 86, 171, 676, 1799, 2962, 4298, 2962, 1799, 676, 171, 342, 1724, 5900, 12179, 19935, 19935, 12179, 5900, 1724, 342, 683, 4501

Offset

1,2

Comments

Table starts

...1....2.....3......6.......11........22.........43.........86........171

...2....4.....8.....17.......45.......103........264........676.......1724

...3....8....21.....54......185.......552.......1799.......5900......19185

...6...17....54....182......812......2962......12179......50196.....205057

..11...45...185....812.....4298.....19935.....102113.....524113....2687777

..22..103...552...2962....19935....117178.....748665....4870988...31483476

..43..264..1799..12179...102113....748665....5930126...48317804..390225796

..86..676..5900..50196...524113...4870988...48317804..495739986.5038813008

.171.1724.19185.205057..2687777..31483476..390225796.5038813008

.342.4501.63834.864270.14197596.210326324.3267809753

Links

R. H. Hardin, Table of n, a(n) for n = 1..144

Formula

Empirical for column k:

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

k=2: [order 11]

k=3: [order 13]

k=4: [order 96]

Example

Some solutions for n=5 k=4
..0..0..0..0..0..0....0..0..0..0..1..1....0..0..0..0..0..0....0..0..0..0..0..0
..0..0..1..1..0..0....0..0..0..0..1..1....0..0..1..1..0..0....0..0..1..1..0..0
..1..1..1..1..1..1....1..1..1..1..0..0....1..1..1..1..1..1....1..1..1..1..1..1
..1..1..1..1..1..1....1..1..1..1..0..0....1..1..1..1..1..1....1..1..1..1..1..1
..0..0..1..1..2..2....0..0..0..0..1..1....0..0..1..1..0..0....2..2..1..1..0..0
..0..0..0..2..2..2....0..0..0..0..1..1....0..0..0..0..0..0....2..2..2..0..0..0
..0..0..0..2..2..2....0..0..0..0..1..1....0..0..0..0..0..0....2..2..2..0..0..0

Crossrefs

Column 1 is A005578

Sequence in context: A317533 A360999 A343299 * A231441 A284199 A284165

Adjacent sequences: A231224 A231225 A231226 * A231228 A231229 A231230

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 05 2013

Status

approved