A316304 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 4, 6 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 12, 12, 8, 16, 24, 20, 24, 16, 32, 64, 39, 39, 64, 32, 64, 184, 110, 114, 110, 184, 64, 128, 432, 245, 339, 339, 245, 432, 128, 256, 1088, 572, 1021, 1519, 1021, 572, 1088, 256, 512, 2944, 1384, 2929, 5120, 5120, 2929, 1384, 2944, 512, 1024, 7360

Offset

1,2

Comments

Table starts

...1....2....4.....8.....16......32.......64.......128........256.........512

...2....4...12....24.....64.....184......432......1088.......2944........7360

...4...12...20....39....110.....245......572......1384.......3267........7767

...8...24...39...114....339....1021.....2929......8639......25410.......74617

..16...64..110...339...1519....5120....19185.....72289.....268933......999260

..32..184..245..1021...5120...20780....97864....444290....2065314.....9512624

..64..432..572..2929..19185...97864...608947...3605691...21632912...130126938

.128.1088.1384..8639..72289..444290..3605691..26898537..208808616..1617004105

.256.2944.3267.25410.268933.2065314.21632912.208808616.2095245767.21106046766

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

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 12] for n>13

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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303794.

Sequence in context: A303800 A305245 A304479 * A304848 A316545 A306060

Adjacent sequences: A316301 A316302 A316303 * A316305 A316306 A316307

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 29 2018

Status

approved