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A305692 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 6 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 152, 98, 3, 5, 383, 1151, 1151, 383, 5, 8, 1493, 8415, 16658, 8415, 1493, 8, 13, 5824, 61796, 236246, 236246, 61796, 5824, 13, 21, 22717, 453553, 3346848, 6433903, 3346848, 453553, 22717, 21, 34, 88609, 3329201 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0.....1........1..........2.............3................5..................8

..1.....7.......25.........98...........383.............1493...............5824

..1....25......152.......1151..........8415............61796.............453553

..2....98.....1151......16658........236246..........3346848...........47448563

..3...383.....8415.....236246.......6433903........175572754.........4791219558

..5..1493....61796....3346848.....175572754.......9226209199.......484920924010

..8..5824...453553...47448563....4791219558.....484920924010.....49083436693252

.13.22717..3329201..672609073..130750175963...25486278629503...4968168200482612

.21.88609.24436772.9534641574.3568076221953.1339494303168987.502868587709213674

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..199

FORMULA

Empirical for column k:

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

k=2: a(n) = 3*a(n-1) +3*a(n-2) +2*a(n-3)

k=3: a(n) = 6*a(n-1) +8*a(n-2) +12*a(n-3) +11*a(n-4) -a(n-5) +a(n-6) +a(n-7) -a(n-8)

k=4: [order 17]

k=5: [order 52]

EXAMPLE

Some solutions for n=5 k=4

..0..0..0..1. .0..0..1..1. .0..0..0..0. .0..0..1..0. .0..0..0..1

..1..0..0..1. .1..0..0..0. .1..1..1..1. .0..1..1..0. .0..1..0..1

..1..0..0..1. .0..0..0..0. .0..0..0..1. .1..0..0..1. .1..0..1..1

..0..1..0..0. .0..0..0..1. .1..1..1..0. .1..0..1..0. .0..0..1..1

..1..1..1..0. .1..0..0..1. .1..0..0..0. .1..0..1..1. .0..1..1..0

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A316282 A305961 A317222 * A317072 A316953 A317733

Adjacent sequences:  A305689 A305690 A305691 * A305693 A305694 A305695

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 08 2018

STATUS

approved

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Last modified September 17 12:45 EDT 2019. Contains 327131 sequences. (Running on oeis4.)