%I #7 Jan 11 2019 15:10:20
%S 96,552,2658,12001,55131,257417,1201970,5597648,26056421,121329295,
%T 565030902,2631278472,12253239453,57060424477,265717806149,
%U 1237389994220,5762253389058,26833543568447,124957900541999,581901431575301
%N Number of (n+1)X(1+1) 0..3 arrays with no 2X2 subblock having the maximum of its diagonal elements greater than the absolute difference of its antidiagonal elements
%C Column 1 of A251167
%H R. H. Hardin, <a href="/A251160/b251160.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A251160/a251160.pdf">Maple-assisted proof of empirical formula</a>
%F Empirical: a(n) = 7*a(n-1) -18*a(n-2) +43*a(n-3) -59*a(n-4) +70*a(n-5) -62*a(n-6) +33*a(n-7) -14*a(n-8) -3*a(n-9) +6*a(n-10) -a(n-11) for n>13.
%F Verified by _Robert Israel_, Jan 11 2019 (See link).
%e Some solutions for n=4
%e ..0..2....2..3....1..2....3..3....1..3....0..3....1..3....1..1....0..3....0..3
%e ..0..0....0..3....0..2....0..2....0..3....0..3....1..2....0..1....1..1....0..0
%e ..3..0....0..3....0..1....0..0....1..1....0..3....1..1....1..0....0..0....2..2
%e ..3..3....3..0....0..1....2..2....0..0....0..1....0..0....1..0....1..1....0..1
%e ..0..1....3..1....1..0....0..0....3..1....0..0....1..0....3..2....0..1....3..1
%p q:= proc(a,b) local a1, a2, b1, b2;
%p a1:= (a-1) mod 4; a2:= (a-1-a1)/4;
%p b1:= (b-1) mod 4; b2:= (b-1-b1)/4;
%p if max(b1,a2) > abs(b2-a1) then 0 else 1 fi
%p end proc:
%p T:= Matrix(16,16,q):
%p u:= Vector(16,1):
%p seq(u^%T . T^n . u, n=1..30); # _Robert Israel_, Jan 11 2019
%Y Cf. A251167.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 30 2014