A320402 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 4, 8, 4, 8, 28, 28, 8, 16, 97, 142, 97, 16, 32, 338, 732, 732, 338, 32, 64, 1178, 3694, 5956, 3694, 1178, 64, 128, 4105, 18754, 46516, 46516, 18754, 4105, 128, 256, 14305, 94842, 368049, 561290, 368049, 94842, 14305, 256, 512, 49850, 480321

Offset

1,2

Comments

Table starts

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

...2.....8......28........97.........338.........1178...........4105

...4....28.....142.......732........3694........18754..........94842

...8....97.....732......5956.......46516.......368049........2908839

..16...338....3694.....46516......561290......6845143.......83509525

..32..1178...18754....368049.....6845143....127789964.....2392115850

..64..4105...94842...2908839....83509525...2392115850....69104597430

.128.14305..480321..22987303..1016183713..44629532699..1987324601389

.256.49850.2431390.181744907.12380173295.834140753692.57271367516963

Links

R. H. Hardin, Table of n, a(n) for n = 1..219

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) +a(n-3) -a(n-4)

k=3: [order 12] for n>14

k=4: [order 40] for n>41

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A318010.

Sequence in context: A299753 A300267 A318016 * A208709 A300472 A326105

Adjacent sequences: A320399 A320400 A320401 * A320403 A320404 A320405

Keyword

nonn,tabl

Author

R. H. Hardin, Oct 12 2018

Status

approved