cp's OEIS Frontend

A271036 Number of 4 X 4 X 4 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.

%I A271036 #8 Jan 30 2019 09:09:43
%S A271036 34,450,3114,15116,58036,188034,535106,1373944,3244098,7143708,
%T A271036 14829100,29262168,55258840,100405196,176323116,300384832,497995586,
%U A271036 805585902,1274479910,1975833860,3006869580,4498661310,6625771230,9618069240
%N A271036 Number of 4 X 4 X 4 triangular 0..n arrays with some element less than a w, nw or ne neighbor exactly once.
%H A271036 R. H. Hardin, <a href="/A271036/b271036.txt">Table of n, a(n) for n = 1..96</a>
%F A271036 Empirical: a(n) = (73/1814400)*n^10 + (169/120960)*n^9 + (1277/60480)*n^8 + (3667/20160)*n^7 + (84829/86400)*n^6 + (3953/1152)*n^5 + (87629/11340)*n^4 + (324707/30240)*n^3 + (104197/12600)*n^2 + (278/105)*n.
%F A271036 Conjectures from _Colin Barker_, Jan 30 2019: (Start)
%F A271036 G.f.: 2*x*(17 + 38*x + 17*x^2 + x^3) / (1 - x)^11.
%F A271036 a(n) = 11*a(n-1) - 55*a(n-2) + 165*a(n-3) - 330*a(n-4) + 462*a(n-5) - 462*a(n-6) + 330*a(n-7) - 165*a(n-8) + 55*a(n-9) - 11*a(n-10) + a(n-11) for n>11.
%F A271036 (End)
%e A271036 Some solutions for n=4:
%e A271036 .....0........2........2........0........0........0........1........1
%e A271036 ....0.1......2.3......2.3......0.0......1.0......0.0......1.1......1.1
%e A271036 ...1.2.1....1.3.3....2.3.3....0.2.1....2.3.4....0.0.1....1.1.1....0.1.2
%e A271036 ..1.3.3.4..4.4.4.4..4.4.4.3..3.3.3.4..4.4.4.4..3.4.3.4..0.3.3.4..2.2.3.4
%Y A271036 Row 4 of A271034.
%K A271036 nonn
%O A271036 1,1
%A A271036 _R. H. Hardin_, Mar 29 2016