A231032 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, 0, 10, 32, 278, 2988, 23058, 199272, 1722118, 14609220, 124974458, 1068235680, 9122055726, 77940647452, 665873921154, 5688536171256, 48598714312182, 415188274268468, 3547028395905802, 30302970815445712, 258884133806216126

Offset

1,3

Comments

Column 3 of A231037.

Links

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

Formula

Empirical: a(n) = 9*a(n-1) -a(n-2) +15*a(n-3) -374*a(n-4) +260*a(n-5) +256*a(n-6) +60*a(n-7) -176*a(n-8) -32*a(n-9).

Empirical g.f.: 2*x^3*(5 - 29*x + 184*x^3 - 148*x^4 - 32*x^5) / (1 - 9*x + x^2 - 15*x^3 + 374*x^4 - 260*x^5 - 256*x^6 - 60*x^7 + 176*x^8 + 32*x^9). - Colin Barker, Feb 09 2018

Example

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

Crossrefs

Sequence in context: A264286 A120969 A265374 * A232009 A137723 A256352

Adjacent sequences: A231029 A231030 A231031 * A231033 A231034 A231035

Keyword

nonn

Author

R. H. Hardin, Nov 03 2013

Status

approved