A318552 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 4 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 1, 1, 1, 3, 1, 2, 6, 6, 2, 3, 10, 5, 10, 3, 5, 21, 21, 21, 21, 5, 8, 46, 44, 64, 44, 46, 8, 13, 102, 106, 219, 219, 106, 102, 13, 21, 220, 258, 589, 842, 589, 258, 220, 21, 34, 491, 600, 1782, 3172, 3172, 1782, 600, 491, 34, 55, 1077, 1476, 5621, 12073, 14760, 12073, 5621

Offset

1,5

Comments

Table starts

..0...1....1.....2......3.......5........8........13.........21..........34

..1...3....6....10.....21......46......102.......220........491........1077

..1...6....5....21.....44.....106......258.......600.......1476........3461

..2..10...21....64....219.....589.....1782......5621......17333.......54199

..3..21...44...219....842....3172....12073.....49181.....191426......766695

..5..46..106...589...3172...14760....67976....337349....1614708.....7855731

..8.102..258..1782..12073...67976...437825...2689769...16069287...100151409

.13.220..600..5621..49181..337349..2689769..21556643..159367978..1242485030

.21.491.1476.17333.191426.1614708.16069287.159367978.1516492860.14741167613

Links

R. H. Hardin, Table of n, a(n) for n = 1..220

Formula

Empirical for column k:

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

k=2: a(n) = a(n-1) +4*a(n-2) -2*a(n-3) -2*a(n-4) +a(n-5) -4*a(n-6) +4*a(n-7) -a(n-8)

k=3: [order 31]

Example

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

Crossrefs

Column 1 is A000045(n-1).

Column 2 is A317857.

Sequence in context: A360634 A317863 A318214 * A183289 A183253 A201675

Adjacent sequences: A318549 A318550 A318551 * A318553 A318554 A318555

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 28 2018

Status

approved