login
Number of (n+1) X (1+1) 0..2 arrays with the upper median equal to the lower median in every 2 X 2 subblock.
1

%I #8 Oct 20 2018 10:24:19

%S 39,181,815,3741,16999,77701,354015,1615917,7368343,33618069,

%T 153332623,699480765,3190600647,14554394789,66389867839,302842866765,

%U 1381428661751,6301472780213,28744467626991,131119492345053,598108270898471

%N Number of (n+1) X (1+1) 0..2 arrays with the upper median equal to the lower median in every 2 X 2 subblock.

%H R. H. Hardin, <a href="/A235974/b235974.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 4*a(n-1) + 7*a(n-2) - 22*a(n-3) + 8*a(n-4).

%F Empirical g.f.: x*(39 + 25*x - 182*x^2 + 72*x^3) / ((1 - 5*x + 2*x^2)*(1 + x - 4*x^2)). - _Colin Barker_, Oct 20 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A235981.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 17 2014