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Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock summing to 4.
1

%I #12 Mar 31 2018 14:33:31

%S 2445,2967,4029,6207,10725,20247,40749,86127,190005,437127,1049469,

%T 2628447,6849285,18479607,51306189,145657167,420452565,1228323687,

%U 3618906909,10724596287,31909543845,95200145367,284543467629

%N Number of (n+1) X 7 0..2 arrays with every 2 X 2 subblock summing to 4.

%C Column 6 of A183632.

%H R. H. Hardin, <a href="/A183629/b183629.txt">Table of n, a(n) for n = 1..200</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).

%F Conjectures from _Colin Barker_, Mar 31 2018: (Start)

%F G.f.: 3*x*(815 - 3901*x + 4374*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

%F a(n) = 3*(644 + 21*2^(2+n) + 3^n).

%F (End)

%e Some solutions for 3 X 7:

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

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

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

%Y Cf. A183632.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 06 2011