cp's OEIS Frontend

A188819 Number of n X 3 binary arrays without the pattern 0 1 diagonally or antidiagonally.

%I A188819 #9 Apr 29 2018 08:46:46
%S A188819 8,25,48,81,120,169,224,289,360,441,528,625,728,841,960,1089,1224,
%T A188819 1369,1520,1681,1848,2025,2208,2401,2600,2809,3024,3249,3480,3721,
%U A188819 3968,4225,4488,4761,5040,5329,5624,5929,6240,6561,6888,7225,7568,7921,8280,8649
%N A188819 Number of n X 3 binary arrays without the pattern 0 1 diagonally or antidiagonally.
%C A188819 Column 3 of A188824.
%H A188819 R. H. Hardin, <a href="/A188819/b188819.txt">Table of n, a(n) for n = 1..200</a>
%F A188819 Empirical: a(n) = 2*a(n-1) - 2*a(n-3) + a(n-4).
%F A188819 Conjectures from _Colin Barker_, Apr 29 2018: (Start)
%F A188819 G.f.: x*(8 + 9*x - 2*x^2 + x^3) / ((1 - x)^3*(1 + x)).
%F A188819 a(n) = (2 + 8*n + 8*n^2) / 2 for n even.
%F A188819 a(n) = (8*n + 8*n^2) / 2 for n odd.
%F A188819 (End)
%e A188819 Some solutions for 4 X 3:
%e A188819 ..1..1..1....1..1..1....1..1..0....1..1..1....1..0..1....0..1..0....0..1..0
%e A188819 ..0..1..1....1..1..1....1..0..1....1..1..1....0..0..0....1..0..1....1..0..1
%e A188819 ..1..0..1....1..0..0....0..1..0....1..1..1....0..0..0....0..0..0....0..1..0
%e A188819 ..0..0..0....0..0..0....0..0..1....1..1..1....0..0..0....0..0..0....1..0..1
%Y A188819 Cf. A188824.
%K A188819 nonn
%O A188819 1,1
%A A188819 _R. H. Hardin_, Apr 11 2011