A317871 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

0, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 2, 0, 0, 4, 6, 6, 4, 0, 0, 9, 4, 26, 4, 9, 0, 0, 22, 5, 88, 88, 5, 22, 0, 0, 53, 10, 301, 220, 301, 10, 53, 0, 0, 130, 36, 1089, 759, 759, 1089, 36, 130, 0, 0, 320, 34, 4340, 3303, 4692, 3303, 4340, 34, 320, 0, 0, 788, 43, 16696, 11807, 27620

Offset

1,12

Comments

Table starts

.0...0..0.....0.....0......0.......0.........0..........0...........0

.0...1..1.....2.....4......9......22........53........130.........320

.0...1..1.....6.....4......5......10........36.........34..........43

.0...2..6....26....88....301....1089......4340......16696.......64514

.0...4..4....88...220....759....3303.....11807......45995......161983

.0...9..5...301...759...4692...27620....167100.....990871.....5767582

.0..22.10..1089..3303..27620..163297...1242087....7872632....53760082

.0..53.36..4340.11807.167100.1242087..13125877..113996501..1068543427

.0.130.34.16696.45995.990871.7872632.113996501.1146051177.13578301848

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)

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 18]

k=4: [order 83] for n>86

Example

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

Crossrefs

Column 2 is A317735.

Sequence in context: A241291 A317741 A317902 * A082995 A079549 A143374

Adjacent sequences: A317868 A317869 A317870 * A317872 A317873 A317874

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 09 2018

Status

approved