A282791 T(n,k)=Number of nXk 0..1 arrays with no 1 equal to more than one of its king-move neighbors, with the exception of exactly one element.

0, 0, 0, 1, 0, 1, 2, 8, 8, 2, 5, 16, 73, 16, 5, 12, 72, 318, 318, 72, 12, 26, 240, 1747, 1952, 1747, 240, 26, 56, 736, 8216, 16584, 16584, 8216, 736, 56, 118, 2352, 38027, 119176, 208559, 119176, 38027, 2352, 118, 244, 7128, 173722, 832218, 2207352, 2207352

Offset

1,7

Comments

Table starts

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

...0.....0.......8........16..........72...........240.............736

...1.....8......73.......318........1747..........8216...........38027

...2....16.....318......1952.......16584........119176..........832218

...5....72....1747.....16584......208559.......2207352........22998587

..12...240....8216....119176.....2207352......34974844.......545174028

..26...736...38027....832218....22998587.....545174028.....12713143876

..56..2352..173722...5780340...236744562....8385651160....292288389872

.118..7128..773529..39020884..2372235577..125782952202...6555156469894

.244.21424.3412416.260919192.23556868268.1869100531456.145619095090322

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: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)

k=3: [order 12]

k=4: [order 18]

k=5: [order 42]

k=6: [order 60]

Example

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

Crossrefs

Column 1 is A073778(n-1).

Sequence in context: A196775 A021351 A011061 * A242168 A011288 A198234

Adjacent sequences: A282788 A282789 A282790 * A282792 A282793 A282794

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 21 2017

Status

approved