A279741 T(n,k)=Number of nXk 0..1 arrays with no element equal to a strict majority of its horizontal and antidiagonal neighbors, with the exception of exactly one element, and with new values introduced in order 0 sequentially upwards.

0, 0, 0, 2, 2, 0, 2, 6, 8, 0, 5, 14, 35, 26, 0, 8, 26, 106, 168, 80, 0, 15, 48, 286, 736, 766, 240, 0, 26, 84, 746, 2948, 4940, 3402, 708, 0, 46, 146, 1887, 11434, 29140, 32430, 14827, 2062, 0, 80, 250, 4700, 42494, 167904, 281350, 209558, 63680, 5944, 0, 139

Offset: 1

Author

R. H. Hardin, Dec 18 2016

Keywords

• nonn
• tabl

Comments

Table starts

.0.....0.......2........2..........5...........8............15..............26

.0.....2.......6.......14.........26..........48............84.............146

.0.....8......35......106........286.........746..........1887............4700

.0....26.....168......736.......2948.......11434.........42494..........154886

.0....80.....766.....4940......29140......167904........927615.........5029822

.0...240....3402....32430.....281350.....2407152......19743140.......158848594

.0...708...14827...209558....2672708....33954530.....413326300......4935790522

.0..2062...63680..1337624...25057618...472691878....8539248826....151323545378

.0..5944..270313..8453760..232453138..6511502806..174560480712...4589874672896

.0.16990.1136546.52990574.2137856646.88926626284.3537506044402.137999764109606

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..199

Crossrefs

Row 1 is A006367(n-1).

Formula

Empirical for column k:

k=1: a(n) = a(n-1)

k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

k=3: a(n) = 10*a(n-1) -35*a(n-2) +54*a(n-3) -45*a(n-4) +20*a(n-5) -4*a(n-6) for n>7

k=4: [order 16] for n>17

k=5: [order 25] for n>26

k=6: [order 64] for n>65

Empirical for row n:

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

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

n=3: [order 16] for n>18

n=4: [order 45] for n>50