A239155 T(n,k)=Number of (n+1)X(k+1) 0..3 arrays with no element equal to all horizontal neighbors or unequal to all vertical neighbors, and new values 0..3 introduced in row major order.
1, 2, 1, 7, 2, 7, 24, 7, 55, 17, 88, 24, 868, 208, 96, 328, 88, 12159, 5775, 2778, 340, 1235, 328, 175471, 135766, 209839, 17050, 1639, 4668, 1235, 2519488, 3313304, 12844591, 2709568, 166531, 6623, 17675, 4668, 36221263, 80240064, 821135900, 330311070
Offset: 1
Examples
Some solutions for n=4 k=4 ..0..1..1..0..2....0..1..1..2..3....0..1..2..0..2....0..1..2..0..3 ..0..1..1..0..2....0..1..1..2..3....0..1..2..0..2....0..1..2..0..3 ..0..1..1..0..2....0..2..1..2..1....2..1..2..1..0....0..1..2..0..3 ..0..3..1..3..1....3..2..0..0..1....2..0..1..1..0....1..2..1..2..3 ..0..3..1..3..1....3..2..0..0..1....2..0..1..1..0....1..2..1..2..3
Links
- R. H. Hardin, Table of n, a(n) for n = 1..113
Crossrefs
Row 1 and 2 are A221454(n+1)
Formula
Empirical for column k:
k=1: a(n) = 4*a(n-1) +7*a(n-2) -26*a(n-3) +5*a(n-4) +14*a(n-5)
k=2: [order 14]
k=3: [order 9]
Empirical for row n:
n=1: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)
n=2: a(n) = 4*a(n-1) +a(n-2) -6*a(n-3) -3*a(n-4)
n=3: a(n) = 14*a(n-1) +14*a(n-2) -124*a(n-3) -6*a(n-4) +90*a(n-5) -27*a(n-6)
n=4: [order 14]
n=5: [order 57]
Comments