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

1,5

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

Links

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

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]

Example

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

Crossrefs

Column 1 is A073778(n-1).

Sequence in context: A030441 A298570 A284771 * A297823 A297993 A298846

Adjacent sequences: A283039 A283040 A283041 * A283043 A283044 A283045

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 27 2017

Status

approved