A253517 - OEIS

%I #7 Mar 20 2018 10:17:33

%S 81,470,2180,9623,42669,192393,876277,4010555,18395493,84458827,

%T 387945181,1782308819,8189083701,37627550715,172896033837,

%U 794452690915,3650504500581,16774075855627,77076986789213,354169411790451

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

%C Column 1 of A253524.

%H R. H. Hardin, <a href="/A253517/b253517.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 8*a(n-1) - 15*a(n-2) - 12*a(n-3) + 44*a(n-4) - 8*a(n-5) - 16*a(n-6) for n>13.

%F Empirical g.f.: x*(81 - 178*x - 365*x^2 + 205*x^3 + 461*x^4 + 1514*x^5 + 1780*x^6 - 190*x^7 - 1648*x^8 - 1440*x^9 - 720*x^10 - 224*x^11 - 32*x^12) / ((1 - x)*(1 - 2*x)*(1 - 5*x - 2*x^2 + 16*x^3 + 8*x^4)). - _Colin Barker_, Mar 20 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Cf. A253524.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 03 2015