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
Keywords
Examples
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
Links
- R. H. Hardin, Table of n, a(n) for n = 1..210
Crossrefs
Cf. A214384.
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)
Comments