A235880 - OEIS

%I #8 Oct 19 2018 09:12:27

%S 339,537,951,1833,3759,8097,18231,42873,105279,269457,715911,1963113,

%T 5520399,15823617,45995991,135038553,399217119,1185854577,3533970471,

%U 10554725193,31569803439,94520666337,283184511351,848798559033

%N Number of (n+1) X (4+1) 0..2 arrays with the minimum plus the upper median equal to the lower median plus the maximum in every 2 X 2 subblock.

%H R. H. Hardin, <a href="/A235880/b235880.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3).

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

%F G.f.: 3*x*(113 - 499*x + 486*x^2) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).

%F a(n) = 3*(50 + 15*2^(1+n) + 3^n).

%F (End)

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 4 of A235884.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 16 2014