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A301790
T(n,k)=Number of nXk 0..1 arrays with every element equal to 0 or 1 horizontally or antidiagonally adjacent elements, with upper left element zero.
12
1, 2, 2, 3, 5, 4, 5, 6, 13, 8, 8, 9, 12, 34, 16, 13, 14, 17, 24, 89, 32, 21, 22, 25, 32, 48, 233, 64, 34, 35, 38, 45, 61, 96, 610, 128, 55, 56, 59, 66, 82, 116, 192, 1597, 256, 89, 90, 93, 100, 116, 150, 221, 384, 4181, 512, 144, 145, 148, 155, 171, 205, 275, 421, 768, 10946
OFFSET
1,2
COMMENTS
Table starts
...1....2...3...5...8...13...21...34...55...89..144...233...377...610...987
...2....5...6...9..14...22...35...56...90..145..234...378...611...988..1598
...4...13..12..17..25...38...59...93..148..237..381...614...991..1601..2588
...8...34..24..32..45...66..100..155..244..388..621...998..1608..2595..4192
..16...89..48..61..82..116..171..260..404..637.1014..1624..2611..4208..6792
..32..233..96.116.150..205..294..438..671.1048.1658..2645..4242..6826.11007
..64..610.192.221.275..364..508..741.1118.1728.2715..4312..6896.11077.17842
.128.1597.384.421.505..648..881.1258.1868.2855.4452..7036.11217.17982.28928
.256.4181.768.802.928.1156.1532.2142.3129.4726.7310.11491.18256.29202.46913
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = 3*a(n-1) -a(n-2)
k=3: a(n) = 2*a(n-1)
k=4: a(n) = a(n-1) +2*a(n-2) -a(n-4)
k=5: a(n) = 2*a(n-1) -a(n-4)
k=6: a(n) = a(n-1) +2*a(n-2) -a(n-4) -a(n-5) -a(n-6)
k=7: a(n) = 2*a(n-1) -a(n-4) -a(n-6)
Empirical for row n:
n=1: a(n) = a(n-1) +a(n-2)
n=2: a(n) = 2*a(n-1) -a(n-3) for n>5
n=3: a(n) = 2*a(n-1) -a(n-3) for n>5
n=4: a(n) = 2*a(n-1) -a(n-3) for n>5
n=5: a(n) = 2*a(n-1) -a(n-3) for n>5
n=6: a(n) = 2*a(n-1) -a(n-3) for n>6
n=7: a(n) = 2*a(n-1) -a(n-3) for n>7
EXAMPLE
Some solutions for n=5 k=4
..0..0..1..0. .0..1..0..1. .0..1..1..0. .0..1..1..0. .0..0..1..0
..1..0..1..1. .0..1..0..0. .0..0..1..0. .0..0..1..0. .1..0..1..1
..1..0..0..1. .0..1..1..0. .1..0..1..0. .1..0..1..1. .1..0..0..1
..1..1..0..0. .0..0..1..0. .0..1..0..1. .1..0..0..1. .1..1..0..1
..0..1..1..0. .1..0..1..0. .0..1..0..0. .1..1..0..1. .0..1..0..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A001519(n+1).
Column 3 is A003945.
Row 1 is A000045(n+1).
Sequence in context: A210212 A209762 A026408 * A301964 A334043 A301884
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Mar 26 2018
STATUS
approved