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A302212
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0, 2 or 3 horizontally, diagonally or antidiagonally adjacent elements, with upper left element zero.
12
1, 1, 2, 1, 2, 4, 1, 11, 2, 8, 1, 13, 16, 3, 16, 1, 34, 5, 47, 6, 32, 1, 65, 32, 7, 147, 10, 64, 1, 123, 22, 111, 18, 386, 21, 128, 1, 266, 72, 80, 448, 55, 1065, 42, 256, 1, 499, 101, 424, 281, 1725, 172, 3063, 86, 512, 1, 1037, 216, 1157, 1868, 1395, 6423, 575, 8624, 179
OFFSET
1,3
COMMENTS
Table starts
...1..1....1....1.....1......1.......1........1........1..........1...........1
...2..2...11...13....34.....65.....123......266......499.......1037........2042
...4..2...16....5....32.....22......72......101......216........486.........968
...8..3...47....7...111.....80.....424.....1157.....2922......12816.......33744
..16..6..147...18...448....281....1868.....6036....16344.....110672......332791
..32.10..386...55..1725...1395...11170....46215...142804....1296927.....3754619
..64.21.1065..172..6423...8756...55922...465040..1136003...19265064....60547641
.128.42.3063..575.24927..43128..291320..3509969..9080114..212347228...786789878
.256.86.8624.1962.96909.234170.1544411.29343177.73189971.2698247985.11028726211
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) -2*a(n-4) +a(n-5)
k=3: [order 9]
k=4: [order 28] for n>32
k=5: [order 37] for n>41
Empirical for row n:
n=1: a(n) = a(n-1)
n=2: a(n) = a(n-1) +3*a(n-2) -4*a(n-4) for n>5
n=3: [order 19] for n>20
n=4: [order 61] for n>62
EXAMPLE
Some solutions for n=5 k=4
..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1
..0..1..0..0. .0..1..0..0. .0..0..1..0. .0..1..0..0. .0..0..1..1
..1..1..1..0. .1..1..1..1. .1..1..1..1. .0..1..0..1. .0..1..1..0
..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1
..0..1..0..0. .0..0..1..0. .0..1..0..0. .0..1..0..0. .0..0..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A240513(n-2).
Row 2 is A297870(n+2).
Sequence in context: A303325 A077901 A105619 * A302460 A303242 A302367
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Apr 03 2018
STATUS
approved