A282523 - OEIS

%I #9 Feb 23 2025 11:21:08

%S 8,43,206,1097,5675,29433,153037,794716,4128244,21444844,111394775,

%T 578646848,3005807582,15613798271,81106596833,421311892656,

%U 2188523765507,11368386235590,59053598944793,306756604030647,1593461123288541

%N Number of n X 3 0..1 arrays with no 1 equal to more than two of its king-move neighbors.

%C Column 3 of A282528.

%H R. H. Hardin, <a href="/A282523/b282523.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 5*a(n-1) +2*a(n-2) -a(n-3) -24*a(n-4) +13*a(n-5) -2*a(n-7) +6*a(n-8).

%F Conjectured g.f.: -x*(8+3*x-25*x^2-11*x^3+13*x^4-2*x^5+4*x^6+6*x^7)/(-1+5*x+2*x^2-x^3-24*x^4+13*x^5-2*x^7+6*x^8). - _R. J. Mathar_, Feb 28 2017

%e Some solutions for n=4:

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

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

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

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

%Y Cf. A282528.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 17 2017