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A214385
Number of 3 X 3 X 3 triangular 0..n arrays with no element lying outside the (possibly reversed) range delimited by its sw and se neighbors, and no element equal to its horizontal neighbors.
1
8, 94, 456, 1506, 3976, 9044, 18480, 34812, 61512, 103202, 165880, 257166, 386568, 565768, 808928, 1133016, 1558152, 2107974, 2810024, 3696154, 4802952, 6172188, 7851280, 9893780, 12359880, 15316938, 18840024, 23012486, 27926536, 33683856
OFFSET
1,1
COMMENTS
Row 3 of A214384.
LINKS
FORMULA
Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (22/9)*n^4 + (25/6)*n^3 + (55/36)*n^2 - (19/30)*n.
Conjectures from Colin Barker, Jul 22 2018: (Start)
G.f.: 2*x*(4 + 19*x - 17*x^2 + 4*x^3) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
(End)
EXAMPLE
Some solutions for n=3:
....2......0......2......1......2......1......2......1......0......2......1
...2.1....3.0....0.2....3.1....2.3....0.1....2.1....2.0....0.2....3.0....1.2
..3.0.3..3.0.1..0.2.0..3.1.2..3.0.3..2.0.3..3.2.0..2.3.0..1.0.2..3.1.0..1.3.2
CROSSREFS
Cf. A214384.
Sequence in context: A299034 A299339 A299846 * A121161 A360200 A098269
KEYWORD
nonn
AUTHOR
R. H. Hardin, Jul 14 2012
STATUS
approved