A253462 - OEIS

%I #10 Dec 14 2018 06:29:41

%S 81,540,3640,24208,162016,1081504,7227096,48272160,322493040,

%T 2154281664,14391427080,96138251504,642233318880,4290297708128,

%U 28660448653048,191460012669504,1279008408531440,8544145042353728,57077359575083624

%N Number of (n+1) X (1+1) 0..2 arrays with every 2 X 2 subblock diagonal maximum minus antidiagonal minimum unequal to its neighbors horizontally, vertically, diagonally and antidiagonally.

%H R. H. Hardin, <a href="/A253462/b253462.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = 2*a(n-1) + 27*a(n-2) + 30*a(n-3) - 7*a(n-4) - 8*a(n-5) - 75*a(n-6) - 48*a(n-7) - 16*a(n-8).

%F Empirical g.f.: x*(81 + 378*x + 373*x^2 - 82*x^3 - 313*x^4 - 916*x^5 - 709*x^6 - 156*x^7) / (1 - 2*x - 27*x^2 - 30*x^3 + 7*x^4 + 8*x^5 + 75*x^6 + 48*x^7 + 16*x^8). - _Colin Barker_, Dec 14 2018

%e Some solutions for n=4:

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

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

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

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

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

%Y Column 1 of A253468.

%K nonn

%O 1,1

%A _R. H. Hardin_, Jan 01 2015