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A207170 Number of 2 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207170 #13 Jun 26 2025 11:22:17
%S A207170 4,16,36,81,169,361,784,1681,3600,7744,16641,35721,76729,164836,
%T A207170 354025,760384,1633284,3508129,7535025,16184529,34762816,74666881,
%U A207170 160376896,344473600,739894401,1589218225,3413480625,7331811876,15747991081
%N A207170 Number of 2 X n 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.
%H A207170 R. H. Hardin, <a href="/A207170/b207170.txt">Table of n, a(n) for n = 1..210</a>
%F A207170 Empirical: a(n) = a(n-1) +a(n-2) +3*a(n-3) +a(n-4) -a(n-5) -a(n-6) for n>7.
%F A207170 G.f: 4*x -x^2*(-16-20*x-29*x^2-4*x^3+13*x^4+9*x^5) / ( (x^3+2*x^2+x-1)*(x^3-x^2-1) ). - _R. J. Mathar_, Aug 10 2017
%F A207170 Empirical: 31*a(n) = 114*A002478(n) +133*A002478(n-1) +55*A002478(n) +10*A077961(n) +32*A077961(n-1) -24*A077961(n-2) for n>1. - _R. J. Mathar_, Nov 09 2018
%e A207170 Some solutions for n=4
%e A207170 ..1..1..1..1....1..0..0..1....0..1..1..0....1..1..1..1....1..0..0..1
%e A207170 ..0..1..1..1....1..0..0..1....0..1..1..0....1..1..1..1....1..1..1..1
%Y A207170 Row 2 of A207169.
%Y A207170 Cf. A002478.
%K A207170 nonn
%O A207170 1,1
%A A207170 _R. H. Hardin_, Feb 15 2012