A184449 - OEIS

%I #8 Apr 12 2018 11:37:51

%S 63,234,864,3159,12879,51759,203391,898857,3877551,16120377,75287475,

%T 340653681,1468371483,7083577089,32959439379,145024403049,

%U 711949718619,3363197265009,14961791864691,74118576012057,352900936009611

%N 1/36 the number of (n+2) X 3 0..2 arrays with each 3 X 3 subblock containing two of one value, two of another, and five of the last.

%C Column 1 of A184457.

%H R. H. Hardin, <a href="/A184449/b184449.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 3*a(n-1) + 162*a(n-3) - 486*a(n-4) - 5832*a(n-6) + 17496*a(n-7).

%F Empirical g.f.: 9*x*(7 + 5*x + 18*x^2 - 1071*x^3 - 432*x^4 - 1458*x^5 + 35964*x^6) / ((1 - 3*x)*(1 - 54*x^3)*(1 - 108*x^3)). - _Colin Barker_, Apr 12 2018

%e Some solutions with a(1,1)=0 for 4 X 3:

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

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

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

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

%Y Cf. A184457.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 14 2011