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.

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

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

R. H. Hardin, Table of n, a(n) for n = 1..337

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

Adjacent sequences: A304601 A304602 A304603 * A304605 A304606 A304607

Keyword

nonn,tabl

Author

R. H. Hardin, May 15 2018

Status

approved