A283572 T(n,k) = Number of n X k 0..1 arrays with no 1 equal to more than one of its horizontal, diagonal and antidiagonal neighbors, with the exception of exactly one element.
0, 0, 0, 1, 4, 0, 2, 26, 16, 0, 5, 72, 169, 68, 0, 12, 282, 674, 1108, 256, 0, 26, 908, 4313, 6812, 6453, 924, 0, 56, 2832, 21186, 67892, 60802, 36038, 3232, 0, 118, 8856, 104464, 509952, 945100, 528436, 194173, 11044, 0, 244, 26750, 513458, 3890056, 10919674
Offset: 1
Examples
Some solutions for n=4, k=4 ..1..1..0..0. .1..1..0..0. .0..0..0..0. .0..1..0..0. .0..0..1..0 ..1..0..0..1. .0..0..0..1. .1..1..0..0. .1..0..0..0. .0..1..1..0 ..0..0..1..0. .0..1..0..1. .1..0..1..0. .0..0..1..1. .1..0..0..0 ..0..0..0..0. .0..1..1..0. .0..0..1..0. .1..0..0..1. .0..0..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..241
Formula
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 4*a(n-1) +2*a(n-2) -12*a(n-3) -11*a(n-4) +4*a(n-5) +6*a(n-6) -a(n-8)
k=3: [order 12]
k=4: [order 16]
k=5: [order 42]
k=6: [order 54]
Empirical for row n:
n=1: a(n) = 2*a(n-1) +a(n-2) -3*a(n-4) -2*a(n-5) -a(n-6)
n=2: a(n) = 2*a(n-1) +5*a(n-2) +2*a(n-3) -17*a(n-4) -24*a(n-5) -16*a(n-6)
n=3: [order 12]
n=4: [order 16]
n=5: [order 42]
n=6: [order 64]
Comments