A297749 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 3 or 4 neighboring 1s.

1, 2, 1, 3, 5, 1, 4, 19, 11, 1, 6, 37, 66, 24, 1, 9, 71, 174, 230, 55, 1, 13, 237, 452, 852, 1142, 123, 1, 19, 715, 2223, 3780, 5396, 4344, 276, 1, 28, 1665, 9733, 28540, 34159, 29773, 16384, 621, 1, 41, 4007, 32213, 187564, 462187, 290114, 162828, 72571, 1395

Offset

1,2

Comments

Table starts

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

.1....5.....19......37........71.........237...........715...........1665

.1...11.....66.....174.......452........2223..........9733..........32213

.1...24....230.....852......3780.......28540........187564........1003470

.1...55...1142....5396.....34159......462187.......5298077.......43194128

.1..123...4344...29773....290114.....6379211.....116064732.....1513886975

.1..276..16384..162828...2561262....92963365....2703029494....57155337030

.1..621..72571..945314..22815719..1407868835...67944280878..2266768029479

.1.1395.287634.5347977.202611948.20923328285.1646896960337.88219789959795

Links

R. H. Hardin, Table of n, a(n) for n = 1..180

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: [order 14]

k=4: [order 40]

k=5: [order 77]

Empirical for row n:

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

n=2: a(n) = 2*a(n-1) -a(n-2) +6*a(n-3) +8*a(n-4) -10*a(n-5) -12*a(n-6)

n=3: [order 19]

n=4: [order 52]

Example

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

Crossrefs

Column 2 is A295091.

Row 1 is A000930(n+1).

Sequence in context: A337883 A202179 A297519 * A173588 A286942 A125076

Adjacent sequences: A297746 A297747 A297748 * A297750 A297751 A297752

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 05 2018

Status

approved