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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. 7
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified May 23 07:54 EDT 2022. Contains 353961 sequences. (Running on oeis4.)