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Number of nX3 n X 3 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order.

Column 3 of A233217

Empirical: a(n) = 127*a(n-1) - 2331*a(n-2) + 2205*a(n-3).

Conjectures from Colin Barker, Oct 10 2018: (Start)

G.f.: 2*x*(3 - 193*x + 840*x^2) / ((1 - x)*(1 - 21*x)*(1 - 105*x)).

a(n) = (105 + 2*3^(2+n)*7^n + 5^(1+n)*21^n) / 168.

(End)

Some solutions for n=3:

Column 3 of A233217.

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R. H. Hardin, <a href="/A233212/b233212.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX3 0..5 arrays with no element x(i,j) adjacent to value 5-x(i,j) horizontally or antidiagonally, top left element zero, and 1 appearing before 2 3 and 4, and 2 appearing before 3 in row major order

6, 376, 35446, 3638416, 380283286, 39892988056, 4187991850726, 439722934529296, 46170567719841766, 4847902462062966136, 509029608397682640406, 53448105729259172362576, 5612051035369765495590646

1,1

Column 3 of A233217

Empirical: a(n) = 127*a(n-1) -2331*a(n-2) +2205*a(n-3)

Some solutions for n=3

..0..1..5....0..1..0....0..1..5....0..0..1....0..1..2....0..1..2....0..0..1

..5..2..2....2..2..0....1..2..1....1..2..1....5..1..2....2..2..2....2..0..1

..1..2..1....1..2..5....5..5..5....4..2..2....0..0..3....2..4..5....1..0..1

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nonn

R. H. Hardin, Dec 06 2013

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