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

1,2

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

Links

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

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]

Example

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

Crossrefs

Column 2 is A202796.

Row 1 is A005251(n+2).

Sequence in context: A071949 A297506 A297720 * A220922 A220993 A219002

Adjacent sequences: A297651 A297652 A297653 * A297655 A297656 A297657

Keyword

nonn,tabl

Author

R. H. Hardin, Jan 02 2018

Status

approved