A297452 - OEIS

%I #8 Feb 28 2019 17:41:07

%S 5,25,92,390,1652,6888,28971,121854,512165,2153841,9057847,38091340,

%T 160192797,673691652,2833214557,11915133080,50109322975,210735765317,

%U 886253689076,3727158731899,15674645707885,65920058839981

%N Number of n X 3 0..1 arrays with every 1 horizontally, diagonally or antidiagonally adjacent to 0 or 2 neighboring 1s.

%H R. H. Hardin, <a href="/A297452/b297452.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) - 3*a(n-2) + 4*a(n-3) - 25*a(n-4) + 10*a(n-5) - 7*a(n-6) + 12*a(n-7).

%F Empirical g.f.: x*(5 - 18*x^2 - 15*x^3 + 3*x^4 + 5*x^5 + 12*x^6) / (1 - 5*x + 3*x^2 - 4*x^3 + 25*x^4 - 10*x^5 + 7*x^6 - 12*x^7). - _Colin Barker_, Feb 28 2019

%e Some solutions for n=7:

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

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

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

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

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

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

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

%Y Column 3 of A297457.

%K nonn

%O 1,1

%A _R. H. Hardin_, Dec 30 2017