cp's OEIS Frontend

A208139 Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A208139 #8 Jun 28 2018 14:35:39
%S A208139 12,144,720,2400,6300,14112,28224,51840,89100,145200,226512,340704,
%T A208139 496860,705600,979200,1331712,1779084,2339280,3032400,3880800,4909212,
%U A208139 6144864,7617600,9360000,11407500,13798512,16574544,19780320,23463900
%N A208139 Number of n X 5 0..1 arrays avoiding 0 0 1 and 0 1 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C A208139 Column 5 of A208142.
%H A208139 R. H. Hardin, <a href="/A208139/b208139.txt">Table of n, a(n) for n = 1..210</a>
%F A208139 Empirical: a(n) = n^5 + 4*n^4 + 5*n^3 + 2*n^2.
%F A208139 Conjectures from _Colin Barker_, Jun 28 2018: (Start)
%F A208139 G.f.: 12*x*(1 + 6*x + 3*x^2) / (1 - x)^6.
%F A208139 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6.
%F A208139 (End)
%e A208139 Some solutions for n=4:
%e A208139 ..0..0..0..0..0....0..0..0..0..0....1..1..1..0..0....1..0..1..0..1
%e A208139 ..1..1..1..0..1....0..1..0..1..0....1..1..0..1..0....0..1..0..1..0
%e A208139 ..1..0..1..0..0....0..1..0..0..0....0..1..0..1..0....0..1..0..1..0
%e A208139 ..1..0..0..0..0....0..1..0..0..0....0..0..0..0..0....0..0..0..0..0
%Y A208139 Cf. A208142.
%K A208139 nonn
%O A208139 1,1
%A A208139 _R. H. Hardin_, Feb 23 2012