A318423 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 2, 3 or 6 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 3, 2, 3, 1, 1, 5, 4, 4, 5, 1, 1, 10, 5, 18, 5, 10, 1, 1, 23, 8, 71, 71, 8, 23, 1, 1, 54, 9, 126, 129, 126, 9, 54, 1, 1, 131, 28, 225, 280, 280, 225, 28, 131, 1, 1, 321, 44, 691, 839, 783, 839, 691, 44, 321, 1, 1, 789, 60, 2116, 2717, 2489, 2489, 2717

Offset

1,5

Comments

Table starts

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

.1...2..2....3....5....10.....23......54.....131......321.......789......1943

.1...2..2....4....5.....8......9......28......44.......60.......118.......256

.1...3..4...18...71...126....225.....691....2116.....6101.....15907.....40782

.1...5..5...71..129...280....839....2717....8803....25414.....74518....227494

.1..10..8..126..280...783...2489....9381...35283...124358....433497...1542555

.1..23..9..225..839..2489..11802...45560..190929...738777...2951001..11787988

.1..54.28..691.2717..9381..45560..236755.1089386..4911132..22619361.104787816

.1.131.44.2116.8803.35283.190929.1089386.5897333.30194599.159545175.842177622

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

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

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

k=3: [order 17] for n>19

k=4: [order 58] for n>62

Example

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

Crossrefs

Column 2 is A317809.

Column 3 is A317810.

Sequence in context: A122632 A176809 A317815 * A318091 A301608 A285521

Adjacent sequences: A318420 A318421 A318422 * A318424 A318425 A318426

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 26 2018

Status

approved