A297519 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1 or 3 neighboring 1s.

1, 2, 1, 3, 5, 1, 4, 17, 11, 1, 6, 33, 49, 24, 1, 9, 65, 128, 177, 55, 1, 13, 193, 363, 624, 727, 123, 1, 19, 529, 1408, 2610, 3383, 2445, 276, 1, 28, 1185, 5079, 15896, 19187, 16173, 8931, 621, 1, 41, 2737, 16104, 85843, 193087, 134123, 80436, 33841, 1395, 1, 60, 7169

Offset

1,2

Comments

Table starts

.1....2......3.......4........6..........9...........13............19

.1....5.....17......33.......65........193..........529..........1185

.1...11.....49.....128......363.......1408.........5079.........16104

.1...24....177.....624.....2610......15896........85843........402072

.1...55....727....3383....19187.....193087......1671315......11283382

.1..123...2445...16173...134123....1995817.....25184119.....253060180

.1..276...8931...80436...956810...22251457....424461759....6257746155

.1..621..33841..406779..6834267..249462938...7287075949..156485261895

.1.1395.120079.2013490.48617437.2728125667.119542912709.3789277002360

Links

R. H. Hardin, Table of n, a(n) for n = 1..241

Formula

Empirical for column k:

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

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

k=3: a(n) = a(n-1) +2*a(n-2) +30*a(n-3) +6*a(n-5) -124*a(n-6) -8*a(n-8) +64*a(n-9)

k=4: [order 32]

k=5: [order 54]

Empirical for row n:

n=1: a(n) = a(n-1) +a(n-3)

n=2: a(n) = a(n-1) +4*a(n-3) +12*a(n-4)

n=3: [order 12]

n=4: [order 31]

n=5: [order 87]

Example

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

Crossrefs

Column 2 is A295091.

Row 1 is A000930(n+1).

Sequence in context: A337884 A337883 A202179 * A297749 A173588 A286942

Adjacent sequences: A297516 A297517 A297518 * A297520 A297521 A297522

Keyword

nonn,tabl

Author

R. H. Hardin, Dec 31 2017

Status

approved