A269214 T(n,k)=Number of nXk 0..3 arrays with some element plus some horizontally, diagonally or antidiagonally adjacent neighbor totalling three exactly once.
0, 4, 0, 24, 96, 0, 108, 768, 1152, 0, 432, 6528, 18048, 11424, 0, 1620, 49536, 308544, 361728, 103488, 0, 5832, 360960, 4744704, 12548544, 6712704, 889056, 0, 20412, 2546304, 70371048, 394072704, 474091776, 118872576, 7375872, 0, 69984, 17563392
Offset: 1
Examples
Some solutions for n=3 k=4 ..2..2..3..2. .2..2..2..3. .0..1..0..2. .0..0..0..2. .2..2..0..0 ..0..2..0..2. .0..0..1..0. .1..1..3..0. .0..1..2..0. .0..0..2..3 ..2..1..0..1. .0..1..0..1. .0..1..0..2. .0..0..0..0. .0..0..1..3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..161
Formula
Empirical for column k:
k=1: a(n) = a(n-1)
k=2: a(n) = 14*a(n-1) -49*a(n-2) for n>3
k=3: a(n) = 30*a(n-1) -237*a(n-2) +180*a(n-3) -36*a(n-4) for n>5
k=4: [order 6] for n>7
k=5: [order 20] for n>21
k=6: [order 42] for n>43
Empirical for row n:
n=1: a(n) = 6*a(n-1) -9*a(n-2)
n=2: a(n) = 10*a(n-1) -13*a(n-2) -60*a(n-3) -36*a(n-4)
n=3: [order 8]
n=4: [order 20]
n=5: [order 52] for n>53
Comments