cp's OEIS Frontend

A214353 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.

%I A214353 #10 Jul 22 2018 08:44:00
%S A214353 26,169,660,1951,4822,10507,20840,38421,66802,110693,176188,271011,
%T A214353 404782,589303,838864,1170569,1604682,2164993,2879204,3779335,4902150,
%U A214353 6289603,7989304,10055005,12547106,15533181,19088524,23296715,28250206
%N A214353 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.
%C A214353 Row 3 of A214352.
%H A214353 R. H. Hardin, <a href="/A214353/b214353.txt">Table of n, a(n) for n = 1..210</a>
%F A214353 Empirical: a(n) = (1/36)*n^6 + (7/15)*n^5 + (25/9)*n^4 + (15/2)*n^3 + (331/36)*n^2 + (151/30)*n + 1.
%F A214353 Conjectures from _Colin Barker_, Jul 22 2018: (Start)
%F A214353 G.f.: x*(26 - 13*x + 23*x^2 - 30*x^3 + 20*x^4 - 7*x^5 + x^6) / (1 - x)^7.
%F A214353 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 A214353 (End)
%e A214353 Some solutions for n=3:
%e A214353 ....1......1......2......1......2......1......3......2......3......2......0
%e A214353 ...2.0....1.1....2.1....1.1....2.2....1.2....3.1....0.3....0.3....1.3....1.0
%e A214353 ..3.2.0..0.3.1..3.1.3..0.3.0..2.2.0..2.1.2..3.1.0..0.3.2..0.1.3..1.2.3..3.1.0
%Y A214353 Cf. A214352.
%K A214353 nonn
%O A214353 1,1
%A A214353 _R. H. Hardin_, Jul 13 2012