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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.
13
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
1,5
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
LINKS
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]
EXAMPLE
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
CROSSREFS
Column 2 is A202973.
Sequence in context: A066094 A160625 A324188 * A010246 A186430 A173889
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 05 2018
STATUS
approved