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

1,3

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

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) = 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

Example

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

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A240513(n-2).

Row 2 is A302368.

Sequence in context: A302460 A303242 A302367 * A302889 A303624 A121439

Adjacent sequences: A303081 A303082 A303083 * A303085 A303086 A303087

Keyword

nonn,tabl

Author

R. H. Hardin, Apr 18 2018

Status

approved