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 #9 Apr 30 2018 14:11:27
%S 16,25,81,256,841,2704,8836,28561,93025,301401,980100,3179089,
%T 10329796,33524100,108889225,353477601,1147922161,3726858304,
%U 12101980081,39292754176,127587553636,414263438689,1345129081209,4367552437161
%N Number of 4 X n binary arrays without the pattern 0 1 diagonally or antidiagonally.
%C Row 4 of A188824.
%H R. H. Hardin, <a href="/A188826/b188826.txt">Table of n, a(n) for n = 1..200</a>
%F Empirical: a(n) = 3*a(n-1) + 5*a(n-2) - 15*a(n-3) + 3*a(n-4) + 5*a(n-5) - a(n-6) for n>7.
%F Empirical g.f.: x*(16 - 23*x - 74*x^2 + 128*x^3 - 5*x^4 - 39*x^5 + 7*x^6) / ((1 - 5*x + 6*x^2 - x^3)*(1 + 2*x - x^2 - x^3)). - _Colin Barker_, Apr 30 2018
%e Some solutions for 4 X 3:
%e ..0..1..1....0..1..0....1..1..1....0..1..0....1..1..0....0..1..0....1..1..1
%e ..0..0..1....1..0..1....1..1..1....0..0..0....1..0..1....1..0..0....1..1..1
%e ..0..0..0....0..0..0....0..0..1....0..0..0....0..1..0....0..0..0....1..1..1
%e ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..1....0..0..0....0..1..1
%Y Cf. A188824.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 11 2011