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.

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

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