A207995 - OEIS

%I #12 Nov 23 2015 05:52:48

%S 16,243,3891,63267,1034073,16932816,277458045,4547477370,74538711609,

%T 1221819475953,20027983390866,328298744831580,5381481886580865,

%U 88213445048426316,1445998260462433698,23702862077090281716

%N Number of nX6 0..2 arrays with new values 0..2 introduced in row major order and no element equal to any horizontal or vertical neighbor (colorings ignoring permutations of colors).

%C Column 6 of A207997.

%H R. H. Hardin, <a href="/A207995/b207995.txt">Table of n, a(n) for n = 1..210</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (30,-291,1278,-2901,3519,-2152,516).

%F a(n) = 30*a(n-1) -291*a(n-2) +1278*a(n-3) -2901*a(n-4) +3519*a(n-5) -2152*a(n-6) +516*a(n-7).

%F G.f.: -x*(16-237*x+1257*x^2-3198*x^3+4206*x^4-2736*x^5+688*x^6) / ( -1+30*x-291*x^2+1278*x^3-2901*x^4+3519*x^5-2152*x^6+516*x^7 ). - _R. J. Mathar_, Nov 23 2015

%e Some solutions for n=4

%e ..0..1..2..0..2..0....0..1..2..0..1..2....0..1..2..0..1..0....0..1..2..0..1..2

%e ..1..0..1..2..0..1....2..0..1..2..0..1....2..0..1..2..0..1....1..0..1..2..0..1

%e ..0..1..0..1..2..0....0..1..2..1..2..0....1..2..0..1..2..0....2..1..2..0..1..2

%e ..1..0..1..2..0..2....1..2..1..2..1..2....2..0..1..0..1..2....0..2..0..1..2..1

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 22 2012