login
Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.
1

%I #7 Sep 07 2018 14:21:37

%S 2,3,9,23,53,113,225,421,745,1255,2025,3147,4733,6917,9857,13737,

%T 18769,25195,33289,43359,55749,70841,89057,110861,136761,167311,

%U 203113,244819,293133,348813,412673,485585,568481,662355,768265,887335,1020757,1169793

%N Number of n X 2 binary arrays indicating whether each 2 X 2 subblock of a larger binary array has lexicographically nondecreasing rows and columns, for some larger (n+1) X 3 binary array with rows and columns of the latter in lexicographically nondecreasing order.

%H R. H. Hardin, <a href="/A227252/b227252.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/60)*n^5 - (1/12)*n^4 + (5/12)*n^3 + (1/12)*n^2 - (13/30)*n + 1 for n>1.

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

%F G.f.: x*(2 - 9*x + 21*x^2 - 26*x^3 + 20*x^4 - 7*x^5 + x^6) / (1 - x)^6.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>7.

%F (End)

%e Some solutions for n=4:

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

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

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

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

%Y Column 2 of A227256.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jul 04 2013