A184031 - OEIS

%I #9 Apr 10 2018 05:26:59

%S 16,28,49,91,169,325,625,1225,2401,4753,9409,18721,37249,74305,148225,

%T 296065,591361,1181953,2362369,4723201,9443329,18883585,37761025,

%U 75515905,151019521,302026753,604028929,1208033281,2416017409,4831985665

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

%C Column 1 of A184039.

%H R. H. Hardin, <a href="/A184031/b184031.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*(16 - 20*x - 35*x^2 + 40*x^3) / ((1 - x)*(1 - 2*x)*(1 - 2*x^2)).

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

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

%F (End)

%e Some solutions for 3 X 2:

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

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

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

%Y Cf. A184039.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 08 2011