A184036 - OEIS

%I #8 Apr 10 2018 05:39:59

%S 325,337,358,400,478,634,934,1534,2710,5062,9718,19030,37558,74614,

%T 148534,296374,591670,1182262,2362678,4723510,9443638,18883894,

%U 37761334,75516214,151019830,302027062,604029238,1208033590,2416017718,4831985974

%N 1/16 the number of (n+1) X 7 0..3 arrays with all 2 X 2 subblocks having the same four values.

%C Column 6 of A184039.

%H R. H. Hardin, <a href="/A184036/b184036.txt">Table of n, a(n) for n = 1..200</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*(325 - 638*x - 653*x^2 + 1276*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

%F a(n) = 9*2^(n/2-1) + 9*2^(n-1) + 310 for n even.

%F a(n) = 9*2^(n-1) + 3*2^((n+1)/2) + 310 for n odd.

%F (End)

%e Some solutions for 3 X 7:

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

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

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

%Y Cf. A184039.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011