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A301323 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 5 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 5
1, 2, 2, 4, 7, 4, 8, 18, 18, 8, 16, 50, 45, 50, 16, 32, 138, 116, 116, 138, 32, 64, 383, 293, 302, 293, 383, 64, 128, 1063, 735, 726, 726, 735, 1063, 128, 256, 2951, 1844, 1709, 1649, 1709, 1844, 2951, 256, 512, 8193, 4626, 3996, 3649, 3649, 3996, 4626, 8193, 512 (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....1024....2048

...2....7....18....50...138...383...1063...2951...8193..22748...63161..175370

...4...18....45...116...293...735...1844...4626..11611..29151...73200..183828

...8...50...116...302...726..1709...3996...9346..21891..51367..120680..283746

..16..138...293...726..1649..3649...8035..17751..39436..88008..197077..442264

..32..383...735..1709..3649..7600..15802..33150..70311.150532..324443..702447

..64.1063..1844..3996..8035.15802..31172..62375.126931.262036..546825.1149471

.128.2951..4626..9346.17751.33150..62375.119694.234839.469777..953721.1956225

.256.8193.11611.21891.39436.70311.126931.234839.446581.869959.1726691.3472128

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..612

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 4*a(n-1) -3*a(n-2) -3*a(n-3) +2*a(n-4) +3*a(n-5) -2*a(n-6) for n>8

k=4: a(n) = 4*a(n-1) -4*a(n-2) +2*a(n-5) -3*a(n-7) +2*a(n-8) +a(n-9) -a(n-10) for n>13

k=5: [order 14] for n>16

k=6: [order 15] for n>19

k=7: [order 23] for n>28

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A280598.

Column 3 is A280599.

Column 4 is A280600.

Sequence in context: A299682 A300314 A280604 * A300498 A300937 A300881

Adjacent sequences:  A301320 A301321 A301322 * A301324 A301325 A301326

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Mar 18 2018

STATUS

approved

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Last modified September 23 16:41 EDT 2020. Contains 337315 sequences. (Running on oeis4.)