A236739 - OEIS

%I #8 Oct 21 2018 13:44:38

%S 81,267,833,2907,10233,37467,139201,526395,2012217,7766523,30188609,

%T 118025307,463513593,1826935707,7221598657,28611883131,113569804473,

%U 451466339643,1796832336449,7158277169307,28539550811769,113856616625883

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

%H R. H. Hardin, <a href="/A236739/b236739.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 7*a(n-1) - 2*a(n-2) - 64*a(n-3) + 53*a(n-4) + 229*a(n-5) - 146*a(n-6) - 364*a(n-7) + 96*a(n-8) + 192*a(n-9).

%F Empirical g.f.: x*(81 - 300*x - 874*x^2 + 2794*x^3 + 4345*x^4 - 7738*x^5 - 10020*x^6 + 5472*x^7 + 6720*x^8) / ((1 - x)*(1 + x)*(1 - 4*x)*(1 - 3*x^2)*(1 - x - 4*x^2)*(1 - 2*x - 4*x^2)). - _Colin Barker_, Oct 21 2018

%e Some solutions for n=5:

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

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

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

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

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

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

%Y Column 1 of A236746.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 30 2014