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A280217
T(n,k) = Number of n X k 0..2 arrays with no element unequal to a strict majority of its horizontal, vertical and antidiagonal neighbors, with the exception of exactly two elements, and with new values introduced in order 0 sequentially upwards.
6
0, 1, 1, 0, 2, 0, 6, 26, 26, 6, 6, 92, 158, 92, 6, 30, 307, 886, 886, 307, 30, 54, 1072, 4382, 7048, 4382, 1072, 54, 158, 3541, 20593, 49328, 49328, 20593, 3541, 158, 342, 11834, 93326, 320755, 474433, 320755, 93326, 11834, 342, 846, 38687, 410789, 2001079
OFFSET
1,5
COMMENTS
Table starts
...0......1.......0.........6..........6.........30.........54........158
...1......2......26........92........307.......1072.......3541......11834
...0.....26.....158.......886.......4382......20593......93326.....410789
...6.....92.....886......7048......49328.....320755....2001079...12072893
...6....307....4382.....49328.....474433....4245153...36290440..298709773
..30...1072...20593....320755....4245153...51995541..607401930.6826834071
..54...3541...93326...2001079...36290440..607401930.9673911703
.158..11834..410789..12072893..298709773.6826834071
.342..38687.1768582..71202942.2400798535
.846.125380.7492763.412532945
LINKS
FORMULA
Empirical for column k:
k=1: a(n) = 3*a(n-1) +3*a(n-2) -11*a(n-3) -6*a(n-4) +12*a(n-5) +8*a(n-6);
k=2: [order 10] for n>14;
k=3: [order 21] for n>28;
k=4: [order 42] for n>51.
EXAMPLE
Some solutions for n=4, k=4
..0..1..0..1. .0..1..1..1. .0..0..0..1. .0..0..1..1. .0..0..0..0
..0..0..0..2. .0..1..1..0. .2..2..1..1. .0..0..1..1. .1..1..0..1
..0..0..2..2. .0..0..2..0. .2..2..1..1. .1..1..0..0. .1..0..0..1
..0..0..2..2. .0..0..0..0. .2..2..0..0. .1..1..0..0. .0..0..1..1
CROSSREFS
Column 1 is A279865.
Sequence in context: A362685 A171734 A278746 * A079203 A151751 A196354
KEYWORD
nonn,tabl
AUTHOR
R. H. Hardin, Dec 29 2016
STATUS
approved