A317741 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 2 or 3 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, 3, 3, 4, 0, 0, 9, 2, 4, 2, 9, 0, 0, 22, 4, 14, 14, 4, 22, 0, 0, 53, 6, 23, 14, 23, 6, 53, 0, 0, 130, 14, 35, 38, 38, 35, 14, 130, 0, 0, 320, 14, 98, 74, 22, 74, 98, 14, 320, 0, 0, 788, 22, 213, 149, 36, 36, 149, 213, 22, 788, 0, 0, 1942, 43

Offset

1,12

Comments

Table starts

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

.0...1..1...2...4...9...22..53..130..320...788..1942..4787..11801..29093

.0...1..1...3...2...4....6..14...14...22....43....68....82....147....246

.0...2..3...4..14..23...35..98..213..448..1053..2285..5170..11442..25631

.0...4..2..14..14..38...74.149..269..662..1294..2721..5911..12084..25175

.0...9..4..23..38..22...36.140..146..218...736..1072..1890...4505...8860

.0..22..6..35..74..36..274.280.1065.1939..5947.13101.35847..83062.222994

.0..53.14..98.149.140..280.676..914.2388..3845.11110.14133..42876..69411

.0.130.14.213.269.146.1065.914.3242.5466.15470.37531.94202.234901.706951

Links

R. H. Hardin, Table of n, a(n) for n = 1..645

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 10] for n>13

k=4: [order 23] for n>26

k=5: [order 33] for n>39

k=6: [order 56] for n>63

k=7: [order 97] for n>108

Example

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

Crossrefs

Sequence in context: A180760 A233270 A241291 * A317902 A317871 A082995

Adjacent sequences: A317738 A317739 A317740 * A317742 A317743 A317744

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 05 2018

Status

approved