cp's OEIS Frontend

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.

%I A214385 #8 Jul 22 2018 08:44:08
%S A214385 8,94,456,1506,3976,9044,18480,34812,61512,103202,165880,257166,
%T A214385 386568,565768,808928,1133016,1558152,2107974,2810024,3696154,4802952,
%U A214385 6172188,7851280,9893780,12359880,15316938,18840024,23012486,27926536,33683856
%N 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.
%C A214385 Row 3 of A214384.
%H A214385 R. H. Hardin, <a href="/A214385/b214385.txt">Table of n, a(n) for n = 1..210</a>
%F A214385 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.
%F A214385 Conjectures from _Colin Barker_, Jul 22 2018: (Start)
%F A214385 G.f.: 2*x*(4 + 19*x - 17*x^2 + 4*x^3) / (1 - x)^7.
%F A214385 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.
%F A214385 (End)
%e A214385 Some solutions for n=3:
%e A214385 ....2......0......2......1......2......1......2......1......0......2......1
%e A214385 ...2.1....3.0....0.2....3.1....2.3....0.1....2.1....2.0....0.2....3.0....1.2
%e A214385 ..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
%Y A214385 Cf. A214384.
%K A214385 nonn
%O A214385 1,1
%A A214385 _R. H. Hardin_, Jul 14 2012