A253526 - OEIS

%I #9 Dec 17 2018 08:24:19

%S 81,459,1963,7253,25165,85663,291511,997121,3427953,11826315,40885971,

%T 141512469,490082653,1697732055,5882051383,20380576545,70618256025,

%U 244694019755,847876017411,2937937280013,10180127318973,35274764991959

%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock antidiagonal maximum minus diagonal minimum nondecreasing horizontally and diagonal maximum minus antidiagonal minimum nondecreasing vertically.

%H R. H. Hardin, <a href="/A253526/b253526.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 22*a(n-2) + 21*a(n-3) + 13*a(n-4) - 46*a(n-5) + 40*a(n-6) - 15*a(n-7) + 2*a(n-8).

%F Empirical g.f.: x*(81 - 189*x + 73*x^2 - 54*x^3 - 365*x^4 + 445*x^5 - 121*x^6 + 18*x^7) / ((1 - x)^4*(1 - 4*x + 7*x^3 - 2*x^4)). - _Colin Barker_, Dec 17 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A253533.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 03 2015