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A318075 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 6, 4, 8, 10, 10, 8, 16, 20, 18, 20, 16, 32, 42, 41, 41, 42, 32, 64, 89, 81, 73, 81, 89, 64, 128, 190, 179, 149, 149, 179, 190, 128, 256, 407, 404, 372, 316, 372, 404, 407, 256, 512, 873, 893, 861, 854, 854, 861, 893, 873, 512, 1024, 1874, 2000, 2016, 2195 (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

...2...6...10...20....42.....89....190.....407......873......1874.......4024

...4..10...18...41....81....179....404.....893.....2000......4516......10125

...8..20...41...73...149....372....861....2016.....4901.....11698......27986

..16..42...81..149...316....854...2195....5752....15565.....41364.....110930

..32..89..179..372...854...3029...9966...31057...102906....339938....1115341

..64.190..404..861..2195...9966..46884..184156...819263...3703730...15865269

.128.407..893.2016..5752..31057.184156..935951..5311510..30435406..167286074

.256.873.2000.4901.15565.102906.819263.5311510.38183961.285095330.2029620744

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..420

FORMULA

Empirical for column k:

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

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

k=3: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -3*a(n-4) -6*a(n-5) +6*a(n-6) for n>10

k=4: [order 18] for n>21

k=5: [order 29] for n>33

k=6: [order 56] for n>61

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000079(n-1).

Column 2 is A317759.

Sequence in context: A089002 A097089 A317764 * A318343 A318024 A320409

Adjacent sequences: A318072 A318073 A318074 * A318076 A318077 A318078

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Aug 15 2018

STATUS

approved

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Last modified April 2 00:42 EDT 2023. Contains 361723 sequences. (Running on oeis4.)