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A304604 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 5 or 6 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 13, 9, 16, 32, 22, 23, 23, 22, 32, 64, 45, 53, 73, 53, 45, 64, 128, 101, 131, 179, 179, 131, 101, 128, 256, 218, 330, 515, 560, 515, 330, 218, 256, 512, 477, 793, 1450, 1726, 1726, 1450, 793, 477, 512, 1024, 1041, 1930, 4024, 5205, 6007 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
Table starts
...1...2....4.....8....16.....32......64......128......256.......512.......1024
...2...4....5.....9....22.....45.....101......218......477......1041.......2270
...4...5...13....23....53....131.....330......793.....1930......4765......11686
...8...9...23....73...179....515....1450.....4024....11122.....31092......86816
..16..22...53...179...560...1726....5205....15474....46577....140882.....425811
..32..45..131...515..1726...6007...19634....66861...231749....813171....2823452
..64.101..330..1450..5205..19634...75463...317420..1356754...5638479...22732759
.128.218..793..4024.15474..66861..317420..1874284.10089904..49126115..230760262
.256.477.1930.11122.46577.231749.1356754.10089904.62934491.341047788.1822167540
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 2*a(n-1)
k=2: a(n) = a(n-1) +3*a(n-2) -2*a(n-4) for n>6
k=3: a(n) = a(n-1) +2*a(n-2) +4*a(n-3) +2*a(n-4) -2*a(n-5) -7*a(n-6) -6*a(n-7) for n>10
k=4: [order 17] for n>22
k=5: [order 33] for n>39
k=6: [order 92] for n>99
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..0..0..0
..0..0..1..1. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..1..1. .0..0..0..1. .0..0..0..0. .0..0..0..0. .0..1..1..0
..1..1..1..1. .1..0..0..0. .0..1..1..0. .0..0..0..1. .0..1..0..1
..1..1..1..1. .0..0..0..0. .0..1..1..0. .0..0..0..0. .0..0..1..1
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A052962 for n>2.
Sequence in context: A319414 A303961 A305340 * A316420 A304926 A306166
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 15 2018
STATUS
approved

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Last modified June 19 18:32 EDT 2024. Contains 373507 sequences. (Running on oeis4.)