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

Author

R. H. Hardin, Nov 05 2013

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A005578

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]