A197213 Number of nX4 0..4 arrays with each element x equal to the number its horizontal and vertical neighbors equal to 4,3,2,1,0 for x=0,1,2,3,4

1, 8, 44, 221, 1175, 5982, 30940, 160438, 828709, 4285218, 22165292, 114628225, 592784354, 3065621155, 15854191220, 81990622115, 424018125103, 2192835511699, 11340373874625, 58647355280660, 303298041583255, 1568522750375630

Offset

1,2

Comments

Every 0 is next to 0 4's, every 1 is next to 1 3's, every 2 is next to 2 2's, every 3 is next to 3 1's, every 4 is next to 4 0's

Column 4 of A197217

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = 3*a(n-1) +4*a(n-2) +36*a(n-3) +23*a(n-4) -19*a(n-5) -278*a(n-6) -219*a(n-7) -224*a(n-8) +504*a(n-9) +774*a(n-10) -707*a(n-11) -3046*a(n-12) -372*a(n-13) +3206*a(n-14) +2421*a(n-15) -1229*a(n-16) -2776*a(n-17) +652*a(n-18) +3427*a(n-19) +377*a(n-20) -3956*a(n-21) -2455*a(n-22) +2524*a(n-23) +3446*a(n-24) +272*a(n-25) -1845*a(n-26) -1309*a(n-27) -17*a(n-28) +555*a(n-29) +412*a(n-30) +114*a(n-31) -27*a(n-32) -35*a(n-33) -13*a(n-34) -2*a(n-35)

Example

Some solutions for n=5
..0..2..2..0....0..0..0..1....2..2..2..0....1..3..1..0....0..0..1..0
..0..2..2..0....0..0..1..3....2..0..2..2....0..1..0..0....0..1..3..1
..0..0..0..0....0..1..0..1....2..0..0..2....0..1..0..0....1..1..3..1
..0..1..0..0....0..3..1..0....2..0..0..2....1..3..2..2....3..1..1..0
..1..3..1..0....0..1..0..0....2..2..2..2....0..1..2..2....1..0..0..0

Crossrefs

Sequence in context: A176688 A272154 A270935 * A198768 A082762 A249794

Adjacent sequences: A197210 A197211 A197212 * A197214 A197215 A197216

Keyword

nonn

Author

R. H. Hardin Oct 11 2011

Status

approved