A297762 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 2, 3 or 4 neighboring 1s.

1, 1, 1, 1, 2, 1, 1, 12, 4, 1, 1, 31, 52, 7, 1, 1, 78, 206, 186, 14, 1, 1, 225, 734, 1181, 1045, 31, 1, 1, 733, 4088, 7081, 10639, 5685, 69, 1, 1, 2305, 24801, 73352, 109228, 90727, 28565, 155, 1, 1, 7156, 130159, 759243, 2263784, 1456855, 720785, 148681, 354, 1, 1

Offset

1,5

Comments

Table starts

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

.1...2.....12.......31.........78...........225.............733

.1...4.....52......206........734..........4088...........24801

.1...7....186.....1181.......7081.........73352..........759243

.1..14...1045....10639.....109228.......2263784........45618455

.1..31...5685....90727....1456855......59707529......2301783905

.1..69..28565...720785...18733087....1504842706....108229776807

.1.155.148681..5909241..251641086...39769163381...5394743533114

.1.354.783104.48847911.3354939709.1043883771677.267870723932943

Links

R. H. Hardin, Table of n, a(n) for n = 1..199

Formula

Empirical for column k:

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

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

k=3: [order 15]

k=4: [order 33]

k=5: [order 78]

Empirical for row n:

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

n=2: a(n) = 4*a(n-1) -3*a(n-2) +a(n-3) +6*a(n-4) -18*a(n-5)

n=3: [order 20]

n=4: [order 52]

Example

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

Crossrefs

Column 2 is A202973.

Sequence in context: A066094 A160625 A324188 * A010246 A186430 A173889

Adjacent sequences: A297759 A297760 A297761 * A297763 A297764 A297765

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2018

Status

approved