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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.
13
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
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
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 02 2018
STATUS
approved