A299675 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 1, 2, 3, 5, 6 or 7 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 26, 26, 8, 16, 88, 94, 88, 16, 32, 298, 372, 372, 298, 32, 64, 1012, 1512, 2009, 1512, 1012, 64, 128, 3440, 6133, 12076, 12076, 6133, 3440, 128, 256, 11700, 24742, 69614, 131420, 69614, 24742, 11700, 256, 512, 39804, 100035, 398314

Offset

1,2

Comments

Table starts

...1.....2......4........8.........16..........32............64.............128

...2.....8.....26.......88........298........1012..........3440...........11700

...4....26.....94......372.......1512........6133.........24742..........100035

...8....88....372.....2009......12076.......69614........398314.........2305246

..16...298...1512....12076.....131420.....1223912......11202963.......109221761

..32..1012...6133....69614....1223912....17105490.....231836591......3441737079

..64..3440..24742...398314...11202963...231836591....4670821739....105367758168

.128.11700.100035..2305246..109221761..3441737079..105367758168...3777344294506

.256.39804.404608.13349305.1053093991.50285500321.2312626806147.130056973753183

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

Formula

Empirical for column k:

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

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

k=3: [order 18] for n>19

k=4: [order 65] for n>66

Example

Some solutions for n=5 k=4
..0..1..0..1. .0..1..1..0. .0..1..0..1. .0..0..0..0. .0..0..1..1
..0..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..0. .1..0..0..0
..1..0..0..1. .1..0..0..1. .1..1..1..0. .0..0..1..1. .0..0..0..0
..1..0..0..0. .0..0..0..0. .0..1..1..1. .0..0..0..1. .0..1..0..0
..0..0..1..1. .0..1..0..1. .0..1..0..0. .1..1..0..1. .0..1..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A298189.

Sequence in context: A299345 A299852 A299008 * A299753 A300267 A318016

Adjacent sequences: A299672 A299673 A299674 * A299676 A299677 A299678

Keyword

nonn,tabl

Author

R. H. Hardin, Feb 16 2018

Status

approved