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A185561 1/4 the number of n X 3 0..3 arrays with no element equal both to the element above and to the element to its left.

%I A185561 #8 Apr 16 2018 09:36:11
%S A185561 16,900,50580,2842560,159749820,8977824540,504547256880,
%T A185561 28355191537860,1593541291098420,89555869973406240,
%U A185561 5032975230384726780,282849573983126145660,15895941831670877597520,893340453575999346503940
%N A185561 1/4 the number of n X 3 0..3 arrays with no element equal both to the element above and to the element to its left.
%C A185561 Column 3 of A185567.
%H A185561 R. H. Hardin, <a href="/A185561/b185561.txt">Table of n, a(n) for n = 1..200</a>
%F A185561 Empirical: a(n) = 57*a(n-1) - 45*a(n-2).
%F A185561 Empirical g.f.: 4*x*(4 - 3*x) / (1 - 57*x + 45*x^2). - _Colin Barker_, Apr 16 2018
%e A185561 Some solutions for 5 X 3 with a(1,1)=0:
%e A185561 ..0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0....0..0..0
%e A185561 ..0..2..2....0..2..0....0..2..0....0..2..2....0..2..0....0..2..0....0..2..0
%e A185561 ..2..0..1....0..1..3....0..2..1....0..3..2....0..1..0....0..3..2....0..2..3
%e A185561 ..0..1..3....2..2..2....1..2..2....3..0..3....3..2..3....0..3..3....0..2..3
%e A185561 ..3..3..0....1..2..0....3..3..3....0..3..1....0..1..0....3..1..0....1..1..3
%Y A185561 Cf. A185567.
%K A185561 nonn
%O A185561 1,1
%A A185561 _R. H. Hardin_, Jan 31 2011