cp's OEIS Frontend

A188861 Number of n X 4 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.

%I A188861 #11 Feb 28 2018 09:55:07
%S A188861 16,41,68,95,122,149,176,203,230,257,284,311,338,365,392,419,446,473,
%T A188861 500,527,554,581,608,635,662,689,716,743,770,797,824,851,878,905,932,
%U A188861 959,986,1013,1040,1067,1094,1121,1148,1175,1202,1229,1256,1283,1310,1337,1364
%N A188861 Number of n X 4 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
%C A188861 Column 4 of A188866.
%H A188861 R. H. Hardin, <a href="/A188861/b188861.txt">Table of n, a(n) for n = 1..200</a>
%F A188861 Empirical: a(n) = 27*n - 13 for n>1.
%F A188861 Conjectures from _Colin Barker_, Feb 28 2018: (Start)
%F A188861 G.f.: x*(16 + 9*x + 2*x^2) / (1 - x)^2.
%F A188861 a(n) = 2*a(n-1) - a(n-2) for n>3.
%F A188861 (End)
%e A188861 Some solutions for 3 X 4:
%e A188861 ..1..1..1..1....1..1..0..1....1..1..1..1....1..0..1..1....1..1..1..1
%e A188861 ..1..1..1..1....0..0..0..0....1..1..1..0....0..0..0..0....0..0..1..0
%e A188861 ..1..0..0..1....0..0..0..0....1..1..0..0....0..0..0..0....0..0..0..0
%t A188861 Join[{16}, Range[41, 7000, 27]] (* _Vladimir Joseph Stephan Orlovsky_, Jul 13 2011 *)
%Y A188861 Cf. A188866.
%K A188861 nonn
%O A188861 1,1
%A A188861 _R. H. Hardin_, Apr 12 2011