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A269084 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.

%I A269084 #8 Jan 19 2019 06:41:44
%S A269084 7,30,114,428,1531,5387,18590,63347,213490,713237,2365217,7794642,
%T A269084 25549763,83359179,270860625,876943006,2830104798,9107202178,
%U A269084 29230933367,93601324315,299085155918,953808773503,3036347307176,9649992762591
%N A269084 Number of n X 3 binary arrays with some element plus some horizontally, vertically or antidiagonally adjacent neighbor totalling two not more than once.
%H A269084 R. H. Hardin, <a href="/A269084/b269084.txt">Table of n, a(n) for n = 1..210</a>
%F A269084 Empirical: a(n) = 2*a(n-1) + 9*a(n-2) - 2*a(n-3) - 33*a(n-4) - 42*a(n-5) - 14*a(n-6) + 10*a(n-7) + 8*a(n-8) - a(n-10).
%F A269084 Empirical g.f.: x*(7 + 16*x - 9*x^2 - 56*x^3 - 60*x^4 - 15*x^5 + 13*x^6 + 8*x^7 - x^8 - x^9) / ((1 + x)^2*(1 - 2*x - 3*x^2 - x^3 + x^4)^2). - _Colin Barker_, Jan 19 2019
%e A269084 Some solutions for n=4:
%e A269084 ..0..0..1. .1..0..0. .0..0..1. .1..0..1. .1..0..0. .1..0..1. .0..0..0
%e A269084 ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..1..1
%e A269084 ..0..0..0. .0..0..0. .0..0..1. .1..0..1. .0..0..1. .0..0..0. .0..0..0
%e A269084 ..0..0..0. .0..0..1. .1..0..1. .0..0..0. .0..0..1. .0..0..1. .0..1..0
%Y A269084 Column 3 of A269089.
%K A269084 nonn
%O A269084 1,1
%A A269084 _R. H. Hardin_, Feb 19 2016