A280673 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal and antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
1, 2, 2, 4, 11, 5, 11, 59, 82, 14, 30, 338, 858, 612, 41, 82, 1917, 10205, 12484, 4568, 122, 224, 10893, 119440, 310365, 181640, 34096, 365, 612, 61880, 1401470, 7533245, 9439606, 2642832, 254496, 1094, 1672, 351541, 16438612, 183331502, 474736149
Offset: 1
Examples
Some solutions for n=3 k=4 ..0..1..0..0. .0..1..0..2. .0..1..0..1. .0..0..1..0. .0..1..1..0 ..0..1..2..1. .2..0..2..1. .0..2..1..0. .2..2..1..1. .2..0..2..0 ..1..2..0..0. .2..1..0..2. .2..0..2..0. .1..0..2..2. .1..0..1..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..97
Formula
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 8*a(n-1) -4*a(n-2) for n>3
k=3: a(n) = 14*a(n-1) +8*a(n-2)
k=4: a(n) = 29*a(n-1) +44*a(n-2) -27*a(n-3) -81*a(n-4) for n>5
k=5: [order 8] for n>9
k=6: [order 20] for n>22
Empirical for row n:
n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
n=2: a(n) = 5*a(n-1) +6*a(n-2) -11*a(n-3) -7*a(n-4) +4*a(n-5) for n>6
n=3: [order 18] for n>20
n=4: [order 73] for n>78
Comments