A278157 T(n,k)=Number of nXk 0..1 arrays with every element both equal and not equal to some elements at offset (-1,-1) (-1,0) (-1,1) (0,-1) (0,1) (1,-1) or (1,0), with upper left element zero.

0, 0, 0, 0, 2, 0, 0, 7, 7, 0, 0, 22, 42, 22, 0, 0, 75, 268, 268, 75, 0, 0, 254, 1759, 3382, 1759, 254, 0, 0, 859, 11675, 43876, 43876, 11675, 859, 0, 0, 2906, 77102, 571214, 1118946, 571214, 77102, 2906, 0, 0, 9831, 509336, 7404889, 28772962, 28772962, 7404889

Offset

1,5

Comments

Table starts

.0....0.......0..........0............0...............0.................0

.0....2.......7.........22...........75.............254...............859

.0....7......42........268.........1759...........11675.............77102

.0...22.....268.......3382........43876..........571214...........7404889

.0...75....1759......43876......1118946........28772962.........736017223

.0..254...11675.....571214.....28772962......1459438050.......73654449669

.0..859...77102....7404889....736017223.....73654449669.....7332741364328

.0.2906..509336...96014730..18830978857...3717851037151...730168696119876

.0.9831.3365082.1245182813.481877272697.187699707259842.72720692813101842

Links

R. H. Hardin, Table of n, a(n) for n = 1..287

Formula

Empirical for column k:

k=2: a(n) = 3*a(n-1) +a(n-2) +a(n-3) for n>4

k=3: [order 14] for n>15

k=4: [order 31]

k=5: [order 89] for n>91

Example

Some solutions for n=4 k=4
..0..1..1..0. .0..0..0..0. .0..0..1..1. .0..1..0..0. .0..0..1..0
..0..0..0..1. .1..1..0..1. .1..1..0..0. .0..1..1..0. .1..0..1..0
..0..1..0..1. .1..0..1..1. .1..0..1..0. .0..1..0..0. .1..1..0..0
..0..1..0..1. .0..0..0..0. .1..1..0..0. .0..0..1..0. .1..0..1..0

Crossrefs

Sequence in context: A094596 A143024 A271971 * A198232 A160213 A354661

Adjacent sequences: A278154 A278155 A278156 * A278158 A278159 A278160

Keyword

nonn,tabl

Author

R. H. Hardin, Nov 13 2016

Status

approved