Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #8 Jun 19 2018 12:28:19
%S 9,81,261,603,1161,1989,3141,4671,6633,9081,12069,15651,19881,24813,
%T 30501,36999,44361,52641,61893,72171,83529,96021,109701,124623,140841,
%U 158409,177381,197811,219753,243261,268389,295191,323721,354033,386181
%N Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
%C Column 4 of A207169.
%H R. H. Hardin, <a href="/A207165/b207165.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 9*n^3 + 9*n - 9.
%F Conjectures from _Colin Barker_, Jun 19 2018: (Start)
%F G.f.: 9*x*(1 + 5*x - x^2 + x^3) / (1 - x)^4.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.
%F (End)
%e Some solutions for n=4:
%e ..1..1..1..1....1..1..0..0....1..1..0..0....0..0..1..1....1..0..0..1
%e ..0..1..1..1....0..1..0..0....0..0..1..0....1..0..0..1....0..1..1..0
%e ..0..1..1..0....0..1..0..0....0..0..1..0....1..0..0..1....0..0..1..0
%e ..0..0..1..0....0..1..0..0....0..0..1..0....1..0..0..1....0..0..1..0
%Y Cf. A207169.
%K nonn
%O 1,1
%A _R. H. Hardin_, Feb 15 2012