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Number of nX2 n X 2 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 2 of A233217

Empirical: a(n) = 35*a(n-1) - 259*a(n-2) + 225*a(n-3).

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

G.f.: x*(2 - 47*x + 165*x^2) / ((1 - x)*(1 - 9*x)*(1 - 25*x)).

a(n) = (75 + 10*9^n + 3*25^n) / 120.

(End)

Some solutions for n=5:

Column 2 of A233217.

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R. H. Hardin, <a href="/A233211/b233211.txt">Table of n, a(n) for n = 1..210</a>

allocated for R. H. Hardin

Number of nX2 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

2, 23, 452, 10313, 249062, 6147803, 152986472, 3818284493, 95399716682, 2384476356383, 59607259863692, 1490139655179473, 37253114806771502, 931324481014849763, 23283081522981304112, 582076763553023143253

1,1

Column 2 of A233217

Empirical: a(n) = 35*a(n-1) -259*a(n-2) +225*a(n-3)

Some solutions for n=5

..0..0....0..1....0..0....0..0....0..0....0..0....0..0....0..1....0..0....0..0

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

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

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

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

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nonn

R. H. Hardin, Dec 06 2013

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