A207165 - OEIS

%I #8 Jun 19 2018 12:28:19

%S 9,81,261,603,1161,1989,3141,4671,6633,9081,12069,15651,19881,24813,

%T 30501,36999,44361,52641,61893,72171,83529,96021,109701,124623,140841,

%U 158409,177381,197811,219753,243261,268389,295191,323721,354033,386181

%N Number of n X 4 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 0 1 vertically.

%C Column 4 of A207169.

%H R. H. Hardin, <a href="/A207165/b207165.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*n^3 + 9*n - 9.

%F Conjectures from _Colin Barker_, Jun 19 2018: (Start)

%F G.f.: 9*x*(1 + 5*x - x^2 + x^3) / (1 - x)^4.

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>4.

%F (End)

%e Some solutions for n=4:

%e ..1..1..1..1....1..1..0..0....1..1..0..0....0..0..1..1....1..0..0..1

%e ..0..1..1..1....0..1..0..0....0..0..1..0....1..0..0..1....0..1..1..0

%e ..0..1..1..0....0..1..0..0....0..0..1..0....1..0..0..1....0..0..1..0

%e ..0..0..1..0....0..1..0..0....0..0..1..0....1..0..0..1....0..0..1..0

%Y Cf. A207169.

%K nonn

%O 1,1

%A _R. H. Hardin_, Feb 15 2012