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A297694
T(n,k)=Number of nXk 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0, 2 or 4 neighboring 1s.
13
2, 3, 4, 5, 8, 8, 8, 26, 19, 16, 13, 60, 95, 48, 32, 21, 176, 293, 415, 120, 64, 34, 436, 1244, 1774, 1801, 299, 128, 55, 1216, 4277, 12214, 10647, 7526, 747, 256, 89, 3120, 16931, 60904, 118791, 61054, 32173, 1865, 512, 144, 8488, 61040, 378611, 858645, 1070635
OFFSET
1,1
COMMENTS
Table starts
...2....3......5........8........13..........21............34.............55
...4....8.....26.......60.......176.........436..........1216...........3120
...8...19.....95......293......1244........4277.........16931..........61040
..16...48....415.....1774.....12214.......60904........378611........2026447
..32..120...1801....10647....118791......858645.......8377550.......66530487
..64..299...7526....61054...1070635....11111767.....165522511.....1927501851
.128..747..32173...358972..10084740...150761147....3487451085....59854521809
.256.1865.137242..2106480..94655971..2038941780...73143230512..1850472873182
.512.4656.583129.12300234.880496222.27303620184.1513232424936.56371834811712
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 2*a(n-1) +a(n-2) +a(n-3) -a(n-4)
k=3: [order 8]
k=4: [order 23]
k=5: [order 38]
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) +4*a(n-2) -6*a(n-3)
n=3: [order 9]
n=4: [order 24]
n=5: [order 60]
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..1. .1..0..1..0. .0..1..0..1. .1..1..0..1. .0..1..0..0
..1..0..1..1. .0..0..0..0. .0..0..0..1. .1..1..0..0. .0..1..0..1
..0..0..0..0. .0..0..1..1. .0..1..0..1. .1..0..1..0. .0..0..0..0
..0..0..0..0. .1..0..1..1. .0..0..0..0. .0..1..0..0. .0..1..1..1
..1..0..0..0. .1..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..1..0
CROSSREFS
Column 1 is A000079.
Column 2 is A295045.
Row 1 is A000045(n+2).
Sequence in context: A185198 A297338 A297457 * A297637 A325415 A331076
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Jan 03 2018
STATUS
approved