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

Author

R. H. Hardin, Aug 15 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A317759.

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