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.

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

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

R. H. Hardin, Table of n, a(n) for n = 1..577

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

Adjacent sequences: A303958 A303959 A303960 * A303962 A303963 A303964

Keyword

nonn,tabl

Author

R. H. Hardin, May 03 2018

Status

approved