A282885 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly one element.

0, 0, 0, 1, 2, 1, 2, 8, 8, 2, 5, 32, 74, 32, 5, 12, 122, 430, 430, 122, 12, 26, 416, 2426, 3762, 2426, 416, 26, 56, 1414, 13062, 34314, 34314, 13062, 1414, 56, 118, 4626, 67676, 286920, 480995, 286920, 67676, 4626, 118, 244, 14930, 342972, 2342046, 6296324

Offset

1,5

Comments

Table starts

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

...0.....2.......8.........32..........122............416.............1414

...1.....8......74........430.........2426..........13062............67676

...2....32.....430.......3762........34314.........286920..........2342046

...5...122....2426......34314.......480995........6296324.........80114311

..12...416...13062.....286920......6296324......128768496.......2561487246

..26..1414...67676....2342046.....80114311.....2561487246......79687436788

..56..4626..342972...18668994....995928444....49811090624....2422749969094

.118.14930.1707597..146171090..12166597450...951678283294...72384911847530

.244.47432.8384136.1129426388.146641882796.17942875499666.2134206947210504

Links

R. H. Hardin, Table of n, a(n) for n = 1..264

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: [order 10]

k=3: [order 22]

k=4: [order 42]

k=5: [order 86]

Example

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

Crossrefs

Column 1 is A073778(n-1).

Sequence in context: A221878 A219109 A137305 * A242841 A143208 A353581

Adjacent sequences: A282882 A282883 A282884 * A282886 A282887 A282888

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 24 2017

Status

approved