A281339 - OEIS

%I #8 Feb 19 2019 00:48:20

%S 4,25,68,193,544,1539,4355,12332,34907,98797,279622,791433,2240071,

%T 6340292,17945485,50792619,143762646,406903731,1151694633,3259740340,

%U 9226322979,26114053785,73912847850,209201878257,592122035615

%N Number of n X 3 0..1 arrays with no element equal to more than three of its king-move neighbors and with new values introduced in order 0 sequentially upwards.

%H R. H. Hardin, <a href="/A281339/b281339.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 3*a(n-1) - a(n-2) - a(n-3) + 7*a(n-4) - a(n-5) + 2*a(n-6) + 2*a(n-7) + 2*a(n-9) for n>10.

%F Empirical g.f.: x*(4 + 13*x - 3*x^2 + 18*x^3 + 30*x^4 - 3*x^5 + 16*x^6 + 9*x^7 + 4*x^8 + 4*x^9) / (1 - 3*x + x^2 + x^3 - 7*x^4 + x^5 - 2*x^6 - 2*x^7 - 2*x^9). - _Colin Barker_, Feb 18 2019

%e Some solutions for n=4:

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

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

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

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

%Y Column 3 of A281344.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 20 2017