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Number of length n+2 0..6 arrays with some pair in every consecutive three terms totalling exactly 6.
Column 6 of A245869
Empirical: a(n) = 3*a(n-1) + 3*a(n-2) - a(n-3) - 9*a(n-4) - 24*a(n-5) + 5*a(n-6).
Empirical g.f.: x*(127 + 112*x - 281*x^2 - 574*x^3 - 1141*x^4 + 245*x^5) / (1 - 3*x - 3*x^2 + x^3 + 9*x^4 + 24*x^5 - 5*x^6). - Colin Barker, Nov 04 2018
Some solutions for n=6:
Column 6 of A245869.
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R. H. Hardin, <a href="/A245867/b245867.txt">Table of n, a(n) for n = 1..210</a>
allocated for R. H. Hardin
Number of length n+2 0..6 arrays with some pair in every consecutive three terms totalling exactly 6
127, 493, 1579, 5515, 18505, 63241, 214315, 729097, 2475985, 8415217, 28590415, 97151683, 330100459, 1121650903, 3811203385, 12950003383, 44002376953, 149514426895, 508030458319, 1726221621517, 5865476355769, 19930126601527
1,1
Column 6 of A245869
Empirical: a(n) = 3*a(n-1) +3*a(n-2) -a(n-3) -9*a(n-4) -24*a(n-5) +5*a(n-6)
Some solutions for n=6
..4....2....1....2....2....5....6....1....2....4....3....4....3....4....6....0
..4....0....1....6....6....4....4....6....1....4....3....2....6....6....0....6
..2....6....5....4....0....1....0....5....5....2....3....3....0....2....1....4
..2....5....2....2....4....5....6....1....1....3....0....3....6....4....5....2
..4....1....1....4....2....1....3....5....1....3....6....6....2....3....1....6
..3....4....4....5....3....2....3....6....5....3....0....0....4....2....5....0
..3....2....5....1....3....5....4....0....0....0....2....2....6....4....1....4
..3....3....2....5....6....1....2....5....1....6....6....6....0....0....4....6
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R. H. Hardin, Aug 04 2014
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