A227265 - OEIS

%I #8 Sep 07 2018 16:51:51

%S 3,8,16,30,54,93,153,241,365,534,758,1048,1416,1875,2439,3123,3943,

%T 4916,6060,7394,8938,10713,12741,15045,17649,20578,23858,27516,31580,

%U 36079,41043,46503,52491,59040,66184,73958,82398,91541,101425,112089,123573

%N Number of n X 2 0,1 arrays indicating 2 X 2 subblocks of some larger (n+1) X 3 binary array having a sum of three or less, with rows and columns of the latter in lexicographically nondecreasing order.

%H R. H. Hardin, <a href="/A227265/b227265.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/24)*n^4 + (1/12)*n^3 - (1/24)*n^2 + (47/12)*n - 1.

%F Conjectures from _Colin Barker_, Sep 07 2018: (Start)

%F G.f.: x*(3 - 7*x + 6*x^2 - x^4) / (1 - x)^5.

%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>5.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A227269.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 04 2013