A305230 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 21, 21, 8, 16, 49, 24, 49, 16, 32, 120, 54, 54, 120, 32, 64, 293, 108, 116, 108, 293, 64, 128, 719, 236, 253, 253, 236, 719, 128, 256, 1774, 509, 541, 757, 541, 509, 1774, 256, 512, 4389, 1091, 1248, 2050, 2050, 1248, 1091, 4389, 512, 1024, 10893

Offset

1,2

Comments

Table starts

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

...2....8...21...49...120....293.....719.....1774......4389......10893

...4...21...24...54...108....236.....509.....1091......2363.......5109

...8...49...54..116...253....541....1248.....2831......6471......14788

..16..120..108..253...757...2050....5958....17002.....49275.....142734

..32..293..236..541..2050...7062...26528....96528....359365....1331372

..64..719..509.1248..5958..26528..135183...656194...3279365...16250652

.128.1774.1091.2831.17002..96528..656194..4217359..28101263..185066191

.256.4389.2363.6471.49275.359365.3279365.28101263.251711366.2221279211

Links

R. H. Hardin, Table of n, a(n) for n = 1..511

Formula

Empirical for column k:

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

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

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

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

k=5: [order 12] for n>16

k=6: [order 17] for n>22

k=7: [order 28] for n>35

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A303721.

Sequence in context: A302820 A303513 A303727 * A304775 A316518 A304472

Adjacent sequences: A305227 A305228 A305229 * A305231 A305232 A305233

Keyword

nonn,tabl

Author

R. H. Hardin, May 27 2018

Status

approved