A303084 T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2, 3, 4 or 6 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.

1, 1, 2, 1, 2, 4, 1, 12, 2, 8, 1, 20, 32, 3, 16, 1, 72, 29, 112, 6, 32, 1, 168, 258, 90, 416, 10, 64, 1, 496, 432, 1455, 304, 1512, 21, 128, 1, 1296, 2525, 3667, 11767, 1054, 5472, 42, 256, 1, 3616, 6313, 33152, 34430, 84474, 4182, 19904, 86, 512, 1, 9760, 30188, 157838

Offset: 1

Author

R. H. Hardin, Apr 18 2018

Keywords

• nonn
• tabl

Comments

Table starts

...1..1.....1.....1........1.........1............1.............1

...2..2....12....20.......72.......168..........496..........1296

...4..2....32....29......258.......432.........2525..........6313

...8..3...112....90.....1455......3667........33152........157838

..16..6...416...304....11767.....34430.......636070.......4585419

..32.10..1512..1054....84474....409478.....13375327.....170974652

..64.21..5472..4182...615471...4862916....266882021....5924274499

.128.42.19904.17369..4647197..60442630...5754725245..218955384065

.256.86.72396.75377.35089147.764631608.125608726910.8100166904419

Examples

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

Links

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

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) -2*a(n-4) +a(n-5)

k=3: [order 11]

k=4: [order 56] for n>57

Empirical for row n:

n=1: a(n) = a(n-1)

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

n=3: [order 17] for n>18

n=4: [order 67] for n>68