A197212 Number of n X 3 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, 5, 14, 44, 149, 479, 1537, 4971, 16088, 52020, 168111, 543379, 1756623, 5678611, 18356490, 59338576, 191817551, 620069245, 2004431603, 6479507953, 20945607368, 67708621756, 218874399841, 707531760601, 2287161925185, 7393462782885

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 3 of A197217.

Links

R. H. Hardin, Table of n, a(n) for n = 1..200

Formula

Empirical: a(n) = 2*a(n-1) +8*a(n-3) +10*a(n-4) +16*a(n-5) +8*a(n-6) +6*a(n-7) -8*a(n-8) -12*a(n-9) -10*a(n-10) -4*a(n-11) -a(n-12).

Empirical g.f.: x*(1 + 3*x + 4*x^2 + 8*x^3 + 11*x^4 + 3*x^5 - x^6 - 5*x^7 - 14*x^8 - 10*x^9 - 5*x^10 - x^11) / (1 - 2*x - 8*x^3 - 10*x^4 - 16*x^5 - 8*x^6 - 6*x^7 + 8*x^8 + 12*x^9 + 10*x^10 + 4*x^11 + x^12). - Colin Barker, May 11 2018

Example

Some solutions for n=4:
..0..1..0....0..0..0....0..0..0....1..3..1....0..0..0....2..2..0....2..2..0
..1..3..1....2..2..2....0..0..0....0..1..0....1..0..0....2..2..0....2..2..0
..2..2..0....2..0..2....0..2..2....0..0..0....3..1..0....0..0..0....0..1..0
..2..2..0....2..2..2....0..2..2....0..0..0....1..0..0....0..0..0....1..3..1

Crossrefs

Cf. A197217.

Sequence in context: A125246 A302762 A140796 * A100059 A270062 A236043

Adjacent sequences: A197209 A197210 A197211 * A197213 A197214 A197215

Keyword

nonn

Author

R. H. Hardin, Oct 11 2011

Status

approved