A281605 T(n,k)=Number of nXk 0..2 arrays with no element equal to more than one of its horizontal, diagonal or antidiagonal neighbors and with new values introduced in order 0 sequentially upwards.
1, 2, 2, 4, 9, 5, 11, 29, 50, 14, 30, 110, 209, 285, 41, 82, 442, 1283, 1623, 1617, 122, 224, 1708, 8180, 16198, 12413, 9188, 365, 612, 6596, 49572, 167545, 203276, 95623, 52193, 1094, 1672, 25624, 302304, 1626073, 3401430, 2563481, 736757, 296511, 3281, 4568
Offset: 1
Examples
Some solutions for n=4 k=4 ..0..0..1..0. .0..1..0..2. .0..1..0..1. .0..1..2..2. .0..1..2..0 ..1..2..2..1. .0..1..0..2. .1..2..0..1. .0..1..0..1. .0..1..0..1 ..0..1..0..1. .2..2..0..1. .1..0..1..2. .0..1..2..1. .2..1..0..1 ..2..1..2..1. .0..1..0..2. .1..2..1..0. .1..2..0..1. .0..1..2..1
Links
- R. H. Hardin, Table of n, a(n) for n = 1..112
Crossrefs
Formula
Empirical for column k:
k=1: a(n) = 4*a(n-1) -3*a(n-2)
k=2: a(n) = 6*a(n-1) -11*a(n-3) +4*a(n-4) for n>5
k=3: a(n) = 7*a(n-1) +10*a(n-2) -26*a(n-3) -64*a(n-4) -40*a(n-5) for n>6
k=4: [order 16] for n>18
k=5: [order 40] for n>42
Empirical for row n:
n=1: a(n) = 2*a(n-1) +2*a(n-2) for n>4
n=2: a(n) = 4*a(n-1) -2*a(n-2) +8*a(n-3) -8*a(n-4) for n>5
n=3: [order 13] for n>15
n=4: [order 55] for n>58
Comments