A305586 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 0, 1, 2, 7 or 8 king-move adjacent elements, with upper left element zero.

1, 2, 2, 4, 4, 4, 8, 3, 3, 8, 16, 5, 6, 5, 16, 32, 8, 8, 8, 8, 32, 64, 13, 19, 15, 19, 13, 64, 128, 21, 33, 38, 38, 33, 21, 128, 256, 34, 60, 102, 76, 102, 60, 34, 256, 512, 55, 112, 247, 327, 327, 247, 112, 55, 512, 1024, 89, 205, 617, 967, 1897, 967, 617, 205, 89, 1024, 2048

Offset

1,2

Comments

Table starts

...1..2...4....8...16.....32......64......128.......256........512........1024

...2..4...3....5....8.....13......21.......34........55.........89.........144

...4..3...6....8...19.....33......60......112.......205........377.........694

...8..5...8...15...38....102.....247......617......1559.......3892........9739

..16..8..19...38...76....327.....967.....2641......8578......26437.......78868

..32.13..33..102..327...1897....8182....33142....152197.....674090.....2919193

..64.21..60..247..967...8182...50618...280791...1818586...11395966....69071165

.128.34.112..617.2641..33142..280791..1944635..17050251..144099899..1144040510

.256.55.205.1559.8578.152197.1818586.17050251.206386330.2422285068.26433099143

Links

R. H. Hardin, Table of n, a(n) for n = 1..420

Formula

Empirical for column k:

k=1: a(n) = 2*a(n-1)

k=2: a(n) = a(n-1) +a(n-2) for n>4

k=3: a(n) = a(n-1) +a(n-2) +a(n-3) for n>5

k=4: a(n) = a(n-1) +2*a(n-2) +5*a(n-3) -2*a(n-5) -4*a(n-6) for n>8

k=5: a(n) = a(n-1) +3*a(n-2) +12*a(n-3) -9*a(n-5) -27*a(n-6) for n>10

k=6: [order 15] for n>20

k=7: [order 45] for n>50

Example

Some solutions for n=5 k=4
..0..0..0..0. .0..0..0..0. .0..0..0..1. .0..0..0..1. .0..0..0..0
..0..0..0..0. .0..0..0..0. .0..0..1..0. .0..0..1..0. .0..1..0..0
..0..0..1..0. .0..0..0..0. .0..0..0..0. .0..0..0..0. .0..0..0..0
..0..0..1..0. .0..1..0..0. .0..0..0..0. .0..1..0..0. .0..1..0..0
..0..0..0..0. .1..0..0..0. .0..0..0..0. .1..0..0..0. .1..0..0..0

Crossrefs

Column 1 is A000079(n-1).

Column 2 is A000045(n+2) for n>2.

Sequence in context: A219156 A210036 A304230 * A305040 A316693 A230014

Adjacent sequences: A305583 A305584 A305585 * A305587 A305588 A305589

Keyword

nonn,tabl

Author

R. H. Hardin, Jun 05 2018

Status

approved