A206336 - OEIS

%I #8 Jun 15 2018 10:39:22

%S 192,96,455,296,1376,880,4111,2622,12319,7854,36945,23550,110823,

%T 70638,332457,211902,997359,635694,2992065,1907070,8976183,5721198,

%U 26928537,17163582,80785599,51490734,242356785,154472190,727070343,463416558

%N Number of (n+1) X 2 0..3 arrays with every 2 X 2 subblock having nonzero determinant and commuting with every horizontal or vertical neighbor.

%C Column 1 of A206343.

%H R. H. Hardin, <a href="/A206336/b206336.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = a(n-1) + 3*a(n-2) - 3*a(n-3) for n>10.

%F Conjectures from _Colin Barker_, Jun 15 2018: (Start)

%F G.f.: x*(192 - 96*x - 217*x^2 + 129*x^3 + 3*x^4 - 19*x^5 - 9*x^6 - x^7 + 4*x^8 + 2*x^9) / ((1 - x)*(1 - 3*x^2)).

%F a(n) = 872 * 3^((n-9)/2+3/2) + 6 for n>7 and even.

%F a(n) = 12313 * 3^((n-9)/2) + 6 for n>7 and odd.

%F (End)

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A206343.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 06 2012