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.

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

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

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

Adjacent sequences: A214382 A214383 A214384 * A214386 A214387 A214388

Keyword

nonn

Author

R. H. Hardin, Jul 14 2012

Status

approved