A231044 Number of n X 3 0..3 arrays x(i,j) with each element horizontally, diagonally or antidiagonally next to at least one element with value (x(i,j)+1) mod 4 and at least one element with value (x(i,j)-1) mod 4, no adjacent elements equal, and upper left element zero.

0, 14, 50, 410, 2430, 16198, 103042, 667690, 4294910, 27706854, 178536322, 1150960010, 7418522110, 47819461126, 308233683970, 1986827617770, 12806735485950, 82550064227622, 532103488349058, 3429848277235530

Offset

1,2

Comments

Column 3 of A231049.

Links

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

Formula

Empirical: a(n) = 3*a(n-1) +19*a(n-2) +19*a(n-3) +12*a(n-4) -8*a(n-5) +8*a(n-6).

Empirical g.f.: 2*x^2*(1 - x)*(7 + 11*x + 8*x^2) / (1 - 3*x - 19*x^2 - 19*x^3 - 12*x^4 + 8*x^5 - 8*x^6). - Colin Barker, Feb 09 2018

Example

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

Crossrefs

Sequence in context: A205354 A281699 A082668 * A231076 A158519 A043132

Adjacent sequences: A231041 A231042 A231043 * A231045 A231046 A231047

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved