A318082 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 3 or 5 horizontally, vertically or antidiagonally adjacent elements, with upper left element zero.

1, 2, 2, 3, 3, 3, 5, 4, 4, 5, 8, 7, 5, 7, 8, 13, 11, 11, 11, 11, 13, 21, 18, 18, 22, 18, 18, 21, 34, 30, 32, 34, 34, 32, 30, 34, 55, 49, 54, 64, 51, 64, 54, 49, 55, 89, 81, 98, 132, 126, 126, 132, 98, 81, 89, 144, 134, 173, 280, 272, 314, 272, 280, 173, 134, 144, 233, 221, 315

Offset

1,2

Comments

Table starts

..1..2...3...5....8...13....21....34.....55.....89.....144.....233......377

..2..3...4...7...11...18....30....49.....81....134.....221.....365......603

..3..4...5..11...18...32....54....98....173....315.....559....1008.....1813

..5..7..11..22...34...64...132...280....556...1083....2208....4480.....9083

..8.11..18..34...51..126...272...616...1347...2910....6602...15218....34152

.13.18..32..64..126..314...699..1778...4262..10254...25322...63395...158636

.21.30..54.132..272..699..1851..5189..13410..35181...97580..275205...756872

.34.49..98.280..616.1778..5189.15876..44305.131008..401009.1258378..3868741

.55.81.173.556.1347.4262.13410.44305.139346.466676.1583947.5508419.18965058

Links

R. H. Hardin, Table of n, a(n) for n = 1..312

Formula

Empirical for column k:

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

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

k=3: [order 24]

Example

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

Crossrefs

Column 1 is A000045(n+1).

Column 2 is A317767.

Sequence in context: A222820 A301662 A317773 * A318350 A127332 A087826

Adjacent sequences: A318079 A318080 A318081 * A318083 A318084 A318085

Keyword

nonn,tabl

Author

R. H. Hardin, Aug 15 2018

Status

approved