A304230 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 3, 3, 8, 16, 5, 5, 5, 16, 32, 8, 6, 6, 8, 32, 64, 13, 11, 11, 11, 13, 64, 128, 21, 16, 20, 20, 16, 21, 128, 256, 34, 22, 46, 31, 46, 22, 34, 256, 512, 55, 33, 97, 89, 89, 97, 33, 55, 512, 1024, 89, 49, 189, 237, 306, 237, 189, 49, 89, 1024, 2048, 144, 71, 395

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..5...6...11...16....22.....33......49.......71......104.......153

...8..5..6..11...20...46....97....189.....395......836.....1701......3492

..16..8.11..20...31...89...237....494....1162.....3043.....7055.....16267

..32.13.16..46...89..306..1047...2561....7117....22405....61758....171188

..64.21.22..97..237.1047..5541..19470...72554...329358..1331161...5120619

.128.34.33.189..494.2561.19470..82029..358328..2197237.11198373..51879617

.256.55.49.395.1162.7117.72554.358328.1842555.14340995.87642095.484603179

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) +a(n-3) for n>5

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

k=5: a(n) = a(n-1) +9*a(n-3) -14*a(n-6) for n>10

k=6: [order 12] for n>18

k=7: [order 45] for n>50

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..0
..1..0..1..1. .0..1..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..1..1..1..1. .0..0..1..0. .0..0..1..0. .0..0..1..0. .0..1..0..0
..1..1..1..1. .0..0..0..0. .0..1..0..0. .0..0..1..0. .0..0..1..0
..1..1..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0

Crossrefs

Column 1 is A000079(n-1).

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

Sequence in context: A115383 A219156 A210036 * A305586 A305040 A316693

Adjacent sequences: A304227 A304228 A304229 * A304231 A304232 A304233

Keyword

nonn,tabl

Author

R. H. Hardin, May 08 2018

Status

approved