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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. 7
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 (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...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

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Last modified September 27 22:36 EDT 2020. Contains 337388 sequences. (Running on oeis4.)