A317238 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 6, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 28, 24, 16, 32, 64, 60, 60, 64, 32, 64, 184, 211, 168, 211, 184, 64, 128, 432, 597, 674, 674, 597, 432, 128, 256, 1088, 1619, 2432, 4798, 2432, 1619, 1088, 256, 512, 2944, 4792, 8255, 24487, 24487, 8255, 4792, 2944, 512, 1024

Offset

1,2

Comments

Table starts

...1....2.....4......8......16.......32........64.........128..........256

...2....4....12.....24......64......184.......432........1088.........2944

...4...12....28.....60.....211......597......1619........4792........13802

...8...24....60....168.....674.....2432......8255.......29245.......105103

..16...64...211....674....4798....24487....112675......602717......3142280

..32..184...597...2432...24487...157007....995887.....7221707.....50355283

..64..432..1619...8255..112675...995887...8436662....83084854....788831052

.128.1088..4792..29245..602717..7221707..83084854..1148371444..15185768273

.256.2944.13802.105103.3142280.50355283.788831052.15185768273.277147933683

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 13] for n>14

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303794.

Sequence in context: A304848 A316545 A306060 * A260038 A193916 A304347

Adjacent sequences: A317235 A317236 A317237 * A317239 A317240 A317241

Keyword

nonn,tabl

Author

R. H. Hardin, Jul 24 2018

Status

approved