cp's OEIS Frontend

A205314 Number of (n+1) X 5 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.

%I A205314 #8 Jun 11 2018 10:51:28
%S A205314 164,1708,18152,193664,2068148,22091516,235994088,2521075824,
%T A205314 26932295140,287714402188,3073619242616,32835119205664,
%U A205314 350773799961748,3747276188396572,40031720975324552,427654276187965520
%N A205314 Number of (n+1) X 5 0..1 arrays with every 2 X 2 subblock having the same number of equal edges, and new values 0..1 introduced in row major order.
%C A205314 Column 4 of A205318.
%H A205314 R. H. Hardin, <a href="/A205314/b205314.txt">Table of n, a(n) for n = 1..210</a>
%F A205314 Empirical: a(n) = 17*a(n-1) -81*a(n-2) +157*a(n-3) -140*a(n-4) +56*a(n-5) -8*a(n-6).
%F A205314 Empirical g.f.: 4*x*(41 - 270*x + 600*x^2 - 580*x^3 + 244*x^4 - 36*x^5) / ((1 - x)*(1 - 16*x + 65*x^2 - 92*x^3 + 48*x^4 - 8*x^5)). - _Colin Barker_, Jun 11 2018
%e A205314 Some solutions for n=4:
%e A205314 ..0..0..1..0..0....0..0..0..0..1....0..1..0..1..0....0..1..0..1..0
%e A205314 ..1..1..1..1..1....0..1..1..0..0....1..1..0..0..0....0..0..0..0..0
%e A205314 ..1..0..0..0..0....1..1..0..0..1....1..0..0..1..0....0..1..1..0..1
%e A205314 ..1..1..1..1..0....0..0..0..1..1....1..1..0..1..1....1..1..0..0..1
%e A205314 ..0..1..0..0..0....1..1..0..0..1....1..0..0..1..0....1..0..0..1..1
%Y A205314 Cf. A205318.
%K A205314 nonn
%O A205314 1,1
%A A205314 _R. H. Hardin_, Jan 25 2012