cp's OEIS Frontend

A184037 1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.

%I A184037 #8 Apr 10 2018 05:55:49
%S A184037 625,637,658,700,778,934,1234,1834,3010,5362,10018,19330,37858,74914,
%T A184037 148834,296674,591970,1182562,2362978,4723810,9443938,18884194,
%U A184037 37761634,75516514,151020130,302027362,604029538,1208033890,2416018018,4831986274
%N A184037 1/16 the number of (n+1) X 8 0..3 arrays with all 2 X 2 subblocks having the same four values.
%C A184037 Column 7 of A184039.
%H A184037 R. H. Hardin, <a href="/A184037/b184037.txt">Table of n, a(n) for n = 1..118</a>
%F A184037 Empirical: a(n) = 3*a(n-1) - 6*a(n-3) + 4*a(n-4).
%F A184037 Conjectures from _Colin Barker_, Apr 10 2018: (Start)
%F A184037 G.f.: x*(625 - 1238*x - 1253*x^2 + 2476*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).
%F A184037 a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 610 for n even.
%F A184037 a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 610 for n odd.
%F A184037 (End)
%e A184037 Some solutions for 3 X 8:
%e A184037 ..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 A184037 ..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 A184037 ..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 A184037 Cf. A184039.
%K A184037 nonn
%O A184037 1,1
%A A184037 _R. H. Hardin_, Jan 08 2011