cp's OEIS Frontend

A188865 Number of n X 8 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.

%I A188865 #9 Feb 28 2018 11:41:22
%S A188865 256,1393,3194,5275,7442,9627,11814,14001,16188,18375,20562,22749,
%T A188865 24936,27123,29310,31497,33684,35871,38058,40245,42432,44619,46806,
%U A188865 48993,51180,53367,55554,57741,59928,62115,64302,66489,68676,70863,73050,75237,77424
%N A188865 Number of n X 8 binary arrays without the pattern 0 1 diagonally, vertically or antidiagonally.
%C A188865 Column 8 of A188866.
%H A188865 R. H. Hardin, <a href="/A188865/b188865.txt">Table of n, a(n) for n = 1..200</a>
%F A188865 Empirical: a(n) = 2187*n - 3495 for n>5.
%F A188865 Conjectures from _Colin Barker_, Feb 28 2018: (Start)
%F A188865 G.f.: x*(256 + 881*x + 664*x^2 + 280*x^3 + 86*x^4 + 18*x^5 + 2*x^6) / (1 - x)^2.
%F A188865 a(n) = 2*a(n-1) - a(n-2) for n>7.
%F A188865 (End)
%e A188865 Some solutions for 3 X 8:
%e A188865 ..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1....1..1..0..1..1..1..1..1
%e A188865 ..1..1..1..1..1..1..1..1....1..1..1..1..1..1..1..1....0..0..0..0..1..1..1..1
%e A188865 ..0..0..0..0..1..1..1..0....0..0..1..0..1..1..1..0....0..0..0..0..0..0..0..0
%Y A188865 Cf. A188866.
%K A188865 nonn
%O A188865 1,1
%A A188865 _R. H. Hardin_, Apr 12 2011