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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified September 30 06:13 EDT 2022. Contains 357099 sequences. (Running on oeis4.)