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

Author

R. H. Hardin, Jan 05 2018

Keywords

• nonn
• tabl

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

Examples

			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
		

Links

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

Crossrefs

Column 2 is A202973.

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]