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A316641 T(n,k)=Number of nXk 0..1 arrays with every element unequal to 1, 2, 3, 5, 7 or 8 king-move adjacent elements, with upper left element zero. 7
0, 1, 1, 1, 7, 1, 2, 16, 16, 2, 3, 45, 43, 45, 3, 5, 120, 122, 122, 120, 5, 8, 333, 404, 524, 404, 333, 8, 13, 928, 1344, 2342, 2342, 1344, 928, 13, 21, 2613, 4583, 9773, 14568, 9773, 4583, 2613, 21, 34, 7400, 15737, 44095, 85222, 85222, 44095, 15737, 7400, 34 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

COMMENTS

Table starts

..0....1.....1......2........3.........5..........8...........13............21

..1....7....16.....45......120.......333........928.........2613..........7400

..1...16....43....122......404......1344.......4583........15737.........53378

..2...45...122....524.....2342......9773......44095.......195387........864584

..3..120...404...2342....14568.....85222.....532401......3294736......20347911

..5..333..1344...9773....85222....684269....5879970.....50360206.....428319949

..8..928..4583..44095...532401...5879970...69857903....835457349....9913271027

.13.2613.15737.195387..3294736..50360206..835457349..14106315869..235116618481

.21.7400.53378.864584.20347911.428319949.9913271027.235116618481.5489873419154

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) = 2*a(n-1) +5*a(n-2) -2*a(n-3) -12*a(n-4) -8*a(n-5) for n>6

k=3: [order 19] for n>21

k=4: [order 69] for n>71

EXAMPLE

Some solutions for n=5 k=4

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

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

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

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

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

CROSSREFS

Column 1 is A000045(n-1).

Column 2 is A304013.

Sequence in context: A304019 A305367 A304959 * A304697 A316448 A316130

Adjacent sequences:  A316638 A316639 A316640 * A316642 A316643 A316644

KEYWORD

nonn,tabl

AUTHOR

R. H. Hardin, Jul 09 2018

STATUS

approved

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Last modified October 22 05:36 EDT 2021. Contains 348160 sequences. (Running on oeis4.)