A297654 T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 1, 2 or 3 neighboring 1s.

1, 2, 1, 4, 10, 1, 7, 43, 36, 1, 12, 140, 231, 126, 1, 21, 494, 1073, 1421, 454, 1, 37, 1845, 6838, 11024, 9033, 1632, 1, 65, 6757, 45036, 131044, 113252, 55706, 5854, 1, 114, 24479, 268655, 1580681, 2525244, 1105531, 346032, 21010, 1, 200, 89068, 1617465

Offset: 1

Author

R. H. Hardin, Jan 02 2018

Keywords

• nonn
• tabl

Comments

Table starts

.1.....2........4..........7...........12.............21................37

.1....10.......43........140..........494...........1845..............6757

.1....36......231.......1073.........6838..........45036............268655

.1...126.....1421......11024.......131044........1580681..........16899640

.1...454.....9033.....113252......2525244.......56630842........1075678445

.1..1632....55706....1105531.....46187510.....1906300826.......63350980838

.1..5854...346032...11089103....864944851....65775301075.....3863740405975

.1.21010..2151932..110654243..16149058068..2265577299182...234680441414485

.1.75412.13364992.1101808354.300870617401.77814433907002.14203234114710492

Examples

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

Links

• R. H. Hardin, Table of n, a(n) for n = 1..219

Crossrefs

Column 2 is A202796.

Row 1 is A005251(n+2).

Formula

Empirical for column k:

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

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

k=3: [order 11]

k=4: [order 24]

k=5: [order 60]

Empirical for row n:

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

n=2: a(n) = 3*a(n-1) -2*a(n-2) +13*a(n-3) +6*a(n-4) +12*a(n-5) +12*a(n-6)

n=3: [order 17]

n=4: [order 38]