A231076 Number of n X 3 0..2 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 3 and at least one element with value (x(i,j)-1) mod 3, and upper left element zero.

0, 14, 50, 784, 5098, 54426, 441392, 4164402, 36112834, 328035136, 2904141306, 26078490234, 232346509536, 2079099213842, 18559730708930, 165899282277744, 1481830921702586, 13241250299275354, 118293782509293488

Offset

1,2

Comments

Column 3 of A231080.

Links

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

Formula

Empirical: a(n) = 6*a(n-1) +37*a(n-2) -99*a(n-3) +4*a(n-4) +287*a(n-5) -808*a(n-6) -1642*a(n-7) +536*a(n-8) +1808*a(n-9) +880*a(n-10) +128*a(n-11).

Empirical g.f.: 2*x^2*(7 - 17*x - 17*x^2 - 35*x^3 - 138*x^4 - 196*x^5 + 408*x^6 + 540*x^7 + 152*x^8) / (1 - 6*x - 37*x^2 + 99*x^3 - 4*x^4 - 287*x^5 + 808*x^6 + 1642*x^7 - 536*x^8 - 1808*x^9 - 880*x^10 - 128*x^11). - Colin Barker, Feb 09 2018

Example

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

Crossrefs

Sequence in context: A281699 A082668 A231044 * A158519 A043132 A039309

Adjacent sequences: A231073 A231074 A231075 * A231077 A231078 A231079

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved