A253742 - OEIS

%I #7 Dec 17 2018 08:23:04

%S 81,450,1998,7803,28107,95940,315576,1011357,3181653,9876870,30368034,

%T 92726271,281717919,852821640,2574980172,7760330145,23356488105,

%U 70229896650,211029428790,633805512579,1902926487411,5711950356300

%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock ne-sw antidiagonal difference nondecreasing horizontally and nw+se diagonal sum nondecreasing vertically.

%H R. H. Hardin, <a href="/A253742/b253742.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 9*a(n-1) - 31*a(n-2) + 51*a(n-3) - 40*a(n-4) + 12*a(n-5).

%F Empirical g.f.: 9*x*(9 - 31*x + 51*x^2 - 40*x^3 + 12*x^4) / ((1 - x)^2*(1 - 2*x)^2*(1 - 3*x)). - _Colin Barker_, Dec 17 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A253749.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 11 2015