A316218 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 5 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 14, 14, 8, 16, 28, 28, 28, 16, 32, 94, 75, 75, 94, 32, 64, 284, 250, 310, 250, 284, 64, 128, 752, 706, 1468, 1468, 706, 752, 128, 256, 2244, 2116, 5883, 8943, 5883, 2116, 2244, 256, 512, 6532, 6399, 25093, 44018, 44018, 25093, 6399, 6532, 512

Offset

1,2

Comments

Table starts

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

...2....4....14.....28......94......284........752........2244.........6532

...4...14....28.....75.....250......706.......2116........6399........19179

...8...28....75....310....1468.....5883......25093......108869.......463940

..16...94...250...1468....8943....44018.....242149.....1355516......7364630

..32..284...706...5883...44018...273102....1906841....13506787.....92623868

..64..752..2116..25093..242149..1906841...17524746...162191532...1448194529

.128.2244..6399.108869.1355516.13506787..162191532..1966735514..22731828021

.256.6532.19179.463940.7364630.92623868.1448194529.22731828021.338897042438

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) +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>16

k=4: [order 62] for n>64

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A304341.

Sequence in context: A260038 A193916 A304347 * A305642 A317036 A305911

Adjacent sequences: A316215 A316216 A316217 * A316219 A316220 A316221

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 26 2018

Status

approved