A305642 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 6 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 29, 28, 16, 32, 94, 78, 78, 94, 32, 64, 284, 255, 334, 255, 284, 64, 128, 752, 743, 1516, 1516, 743, 752, 128, 256, 2244, 2197, 6329, 8734, 6329, 2197, 2244, 256, 512, 6532, 6663, 27110, 48567, 48567, 27110, 6663, 6532, 512

Offset

1,2

Comments

Table starts

...1....2.....4......8.......16........32.........64..........128

...2....4....14.....28.......94.......284........752.........2244

...4...14....29.....78......255.......743.......2197.........6663

...8...28....78....334.....1516......6329......27110.......118085

..16...94...255...1516.....8734.....48567.....282463......1774950

..32..284...743...6329....48567....385282....3252937.....29925524

..64..752..2197..27110...282463...3252937...42274045....591351392

.128.2244..6663.118085..1774950..29925524..591351392..12972861669

.256.6532.20052.519355.11228442.280854245.8584480725.293775609320

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = 2*a(n-1) +2*a(n-2) +6*a(n-3) -10*a(n-4) -8*a(n-5) for n>6

k=3: [order 15] for n>17

k=4: [order 65] for n>67

Example

Some solutions for n=5 k=4
..0..0..1..0. .0..0..1..0. .0..0..1..1. .0..0..0..0. .0..1..1..1
..0..0..0..1. .1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..1..1
..0..0..0..0. .0..0..0..0. .0..0..0..0. .1..0..0..0. .0..0..1..1
..1..0..0..0. .0..0..0..0. .0..0..1..1. .0..0..0..1. .0..0..1..1
..1..0..0..0. .1..1..0..0. .1..1..1..1. .0..0..0..1. .0..0..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A193916 A304347 A316218 * A317036 A305911 A317153

Adjacent sequences: A305639 A305640 A305641 * A305643 A305644 A305645

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 07 2018

Status

approved