A305040 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 3, 3, 8, 16, 5, 7, 5, 16, 32, 8, 7, 7, 8, 32, 64, 13, 13, 19, 13, 13, 64, 128, 21, 23, 26, 26, 23, 21, 128, 256, 34, 37, 61, 43, 61, 37, 34, 256, 512, 55, 63, 143, 109, 109, 143, 63, 55, 512, 1024, 89, 109, 277, 319, 362, 319, 277, 109, 89, 1024, 2048, 144

Offset

1,2

Comments

Table starts

...1..2...4...8...16...32.....64....128.....256......512......1024.......2048

...2..4...3...5....8...13.....21.....34......55.......89.......144........233

...4..3...7...7...13...23.....37.....63.....109......183.......309........527

...8..5...7..19...26...61....143....277.....568.....1244......2600.......5369

..16..8..13..26...43..109....319....718....1632.....4351.....10773......25199

..32.13..23..61..109..362...1359...3503....9721....31745.....92958.....264320

..64.21..37.143..319.1359...7757..28535..104561...483316...2036051....7957330

.128.34..63.277..718.3503..28535.135992..601711..3666530..20376186..100132274

.256.55.109.568.1632.9721.104561.601711.3230419.25079880.172103176.1036410400

Links

R. H. Hardin, Table of n, a(n) for n = 1..449

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +a(n-2) for n>4

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

k=4: a(n) = a(n-1) +5*a(n-3) +a(n-4) -4*a(n-6) -4*a(n-7) for n>11

k=5: a(n) = a(n-1) +9*a(n-3) +2*a(n-4) -14*a(n-6) -4*a(n-7) for n>11

k=6: [order 13] for n>19

k=7: [order 46] for n>51

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A000045(n+1) for n>2.

Sequence in context: A210036 A304230 A305586 * A316693 A230014 A319414

Adjacent sequences: A305037 A305038 A305039 * A305041 A305042 A305043

Keyword

nonn,tabl

Author

R. H. Hardin, May 24 2018

Status

approved