A283042 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal and vertical neighbors, with the exception of exactly one element.

0, 0, 0, 1, 4, 1, 2, 16, 16, 2, 5, 68, 119, 68, 5, 12, 256, 818, 818, 256, 12, 26, 924, 5065, 9152, 5065, 924, 26, 56, 3232, 30378, 94368, 94368, 30378, 3232, 56, 118, 11044, 175963, 931844, 1604067, 931844, 175963, 11044, 118, 244, 37104, 997302, 8912378

Offset: 1

Author

R. H. Hardin, Feb 27 2017

Keywords

• nonn
• tabl

Comments

Table starts

...0......0........1..........2.............5..............12................26

...0......4.......16.........68...........256.............924..............3232

...1.....16......119........818..........5065...........30378............175963

...2.....68......818.......9152.........94368..........931844...........8912378

...5....256.....5065......94368.......1604067........26180826.........414085368

..12....924....30378.....931844......26180826.......706205768.......18455711930

..26...3232...175963....8912378.....414085368.....18455711930......797350288363

..56..11044...997302...83420984....6406597648....471954803540....33705434438284

.118..37104..5559013..767704036...97480211225..11868995624930..1401215705047092

.244.122984.30578068.6973000128.1463896864692.294610925837548.57496998569457406

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..220

Crossrefs

Column 1 is A073778(n-1).

Formula

Empirical for column k:

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

k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)

k=3: [order 18]

k=4: [order 30]

k=5: [order 72]