A269084 - OEIS

%I #8 Jan 19 2019 06:41:44

%S 7,30,114,428,1531,5387,18590,63347,213490,713237,2365217,7794642,

%T 25549763,83359179,270860625,876943006,2830104798,9107202178,

%U 29230933367,93601324315,299085155918,953808773503,3036347307176,9649992762591

%N 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 R. H. Hardin, <a href="/A269084/b269084.txt">Table of n, a(n) for n = 1..210</a>

%F 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 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 Some solutions for n=4:

%e ..0..0..1. .1..0..0. .0..0..1. .1..0..1. .1..0..0. .1..0..1. .0..0..0

%e ..0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..0. .0..0..1. .0..1..1

%e ..0..0..0. .0..0..0. .0..0..1. .1..0..1. .0..0..1. .0..0..0. .0..0..0

%e ..0..0..0. .0..0..1. .1..0..1. .0..0..0. .0..0..1. .0..0..1. .0..1..0

%Y Column 3 of A269089.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 19 2016