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.

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

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