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A316282 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 4, 5 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 25, 25, 2, 3, 98, 125, 98, 3, 5, 383, 846, 846, 383, 5, 8, 1493, 5321, 9540, 5321, 1493, 8, 13, 5824, 34017, 102072, 102072, 34017, 5824, 13, 21, 22717, 216805, 1099200, 1820908, 1099200, 216805, 22717, 21, 34, 88609, 1382759 (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.....125........846.........5321..........34017...........216805

..2....98.....846.......9540.......102072........1099200.........11834419

..3...383....5321.....102072......1820908.......32932624........594230641

..5..1493...34017....1099200.....32932624.....1000914270......30350372014

..8..5824..216805...11834419....594230641....30350372014....1545539179382

.13.22717.1382759..127394654..10728510594...920820679433...78766985363848

.21.88609.8818011.1371525369.193678113501.27936246990475.4013958393240781

LINKS

R. H. Hardin, Table of n, a(n) for n = 1..180

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: [order 9] for n>10

k=4: [order 27] for n>28

k=5: [order 95] for n>97

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304421.

Sequence in context: A306143 A317376 A304427 * A305961 A317222 A305692

Adjacent sequences: A316279 A316280 A316281 * A316283 A316284 A316285

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jun 28 2018

STATUS

approved

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Last modified January 26 20:01 EST 2023. Contains 359833 sequences. (Running on oeis4.)