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1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.
2

%I #8 Apr 10 2018 05:55:49

%S 625,637,658,700,778,934,1234,1834,3010,5362,10018,19330,37858,74914,

%T 148834,296674,591970,1182562,2362978,4723810,9443938,18884194,

%U 37761634,75516514,151020130,302027362,604029538,1208033890,2416018018,4831986274

%N 1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.

%C Column 7 of A184039.

%H R. H. Hardin, <a href="/A184037/b184037.txt">Table of n, a(n) for n = 1..118</a>

%F Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).

%F Conjectures from _Colin Barker_, Apr 10 2018: (Start)

%F G.f.: x*(625 - 1238*x - 1253*x^2 + 2476*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 610 for n even.

%F a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 610 for n odd.

%F (End)

%e Some solutions for 3 X 8:

%e ..2..2..2..2..2..2..2..1....0..0..3..2..0..2..0..2....2..3..2..3..1..3..2..3

%e ..3..1..3..1..3..1..3..2....3..2..0..0..3..0..3..0....1..2..1..2..2..2..1..2

%e ..2..2..2..2..2..2..2..1....0..0..3..2..0..2..0..2....2..3..2..3..1..3..2..3

%Y Cf. A184039.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011