A232060 Number of n X 3 0..2 arrays with every 0 next to a 1 and every 1 next to a 2 horizontally or vertically, with no adjacent values equal.

4, 14, 46, 130, 410, 1194, 3722, 10942, 33806, 100142, 307418, 915594, 2797794, 8365310, 25477518, 76390718, 232103802, 697334282, 2115143362, 6363967678, 19279364750, 58067541662, 175757663194, 529761502474, 1602452666114

Offset

1,1

Links

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

Formula

Empirical: a(n) = a(n-1) + 7*a(n-2) - 3*a(n-3) + 3*a(n-4) - 7*a(n-5) + 2*a(n-6) - 2*a(n-7) + 2*a(n-8).

Empirical g.f.: 2*x*(1 + x + x^2)*(2 + 3*x - 3*x^2 - x^3 - 2*x^4 + 2*x^5) / (1 - x - 7*x^2 + 3*x^3 - 3*x^4 + 7*x^5 - 2*x^6 + 2*x^7 - 2*x^8). - Colin Barker, Oct 03 2018

Example

Some solutions for n=7:
..2..0..2....0..1..0....0..1..2....2..1..0....1..2..1....1..2..1....1..2..1
..0..1..0....1..2..1....2..0..1....1..0..1....0..1..0....2..1..0....0..1..0
..1..2..1....2..1..2....0..2..0....2..1..2....1..2..1....1..0..1....1..0..1
..2..1..0....1..2..1....1..0..1....1..0..1....2..1..2....0..1..2....2..1..2
..0..2..1....0..1..2....2..1..2....0..1..2....1..2..1....2..0..1....1..0..1
..1..0..2....1..2..1....1..0..1....1..2..1....0..1..2....1..2..0....0..1..0
..2..1..0....0..1..0....2..1..2....2..1..2....1..2..1....2..1..2....1..2..1

Crossrefs

Column 3 of A232065.

Sequence in context: A255678 A153480 A229007 * A302238 A171851 A117916

Adjacent sequences: A232057 A232058 A232059 * A232061 A232062 A232063

Keyword

nonn

Author

R. H. Hardin, Nov 17 2013

Status

approved