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A303961 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2 or 5 king-move adjacent elements, with upper left element zero. 7
1, 2, 2, 4, 4, 4, 8, 5, 5, 8, 16, 9, 11, 9, 16, 32, 22, 22, 22, 22, 32, 64, 45, 49, 61, 49, 45, 64, 128, 101, 119, 159, 159, 119, 101, 128, 256, 218, 287, 452, 480, 452, 287, 218, 256, 512, 477, 664, 1228, 1431, 1431, 1228, 664, 477, 512, 1024, 1041, 1563, 3334, 4137, 4645 (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...11...22....49....119....287.....664.....1563.....3716......8788
...8...9...22...61...159....452...1228....3334.....9109....24981.....68361
..16..22...49..159...480...1431...4137...12066....35589...104863....307928
..32..45..119..452..1431...4645..14067...44800...144844...468709...1496959
..64.101..287.1228..4137..14067..44492..156214...557417..1956218...6716752
.128.218..664.3334.12066..44800.156214..702361..2966679.11999856..46586544
.256.477.1563.9109.35589.144844.557417.2966679.14109468.62556978.267420497
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) +3*a(n-3) +2*a(n-4) -2*a(n-5) -6*a(n-6) -4*a(n-7) for n>8
k=4: [order 13] for n>17
k=5: [order 15] for n>21
k=6: [order 32] for n>38
k=7: [order 65] for n>71
EXAMPLE
Some solutions for n=5 k=4
..0..0..0..0. .0..1..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0
..0..0..0..0. .0..0..0..1. .0..0..0..0. .1..0..0..0. .0..0..0..0
..0..0..0..0. .1..0..0..0. .0..0..0..1. .0..0..0..0. .0..0..0..1
..0..0..0..0. .0..0..0..1. .1..0..0..0. .0..0..0..0. .1..0..0..0
..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..0..1..0
CROSSREFS
Column 1 is A000079(n-1).
Column 2 is A052962 for n>2.
Sequence in context: A316693 A230014 A319414 * A305340 A304604 A316420
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, May 03 2018
STATUS
approved

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Last modified May 23 20:54 EDT 2024. Contains 372765 sequences. (Running on oeis4.)