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%I #12 Jul 30 2019 10:13:04
%S 1824,10972,61896,403108,2384304,16476460,100402408,727727388,
%T 4526565112,34009964384,214493580576,1653020851316,10519851847336,
%U 82472356844020,527892783810376,4185126298632084,26885993638734088,214690431691380868
%N Number of (n+1) X (3+1) 0..5 arrays with every 2 X 2 subblock having the sum of the squares of all six edge and diagonal differences equal to 11.
%H R. H. Hardin, <a href="/A233813/b233813.txt">Table of n, a(n) for n = 1..210</a>
%H R. H. Hardin, <a href="/A233813/a233813.txt">Empirical recurrence of order 78</a>
%H Robert Israel, <a href="/A233813/a233813.pdf">Maple-assisted proof of empirical recurrence</a>
%F Empirical recurrence of order 78 (see link above).
%F Empirical recurrence verified (see link). - _Robert Israel_, Jul 30 2019
%e Some solutions for n=3
%e ..1..2..1..0....3..4..3..2....3..4..3..4....2..0..2..0....1..1..2..1
%e ..0..0..0..2....4..2..2..4....4..2..4..2....1..0..1..0....2..3..3..3
%e ..1..2..1..0....4..3..4..3....2..3..2..3....0..2..2..2....2..4..5..4
%e ..2..0..2..0....2..4..2..4....1..1..1..3....1..0..1..0....2..3..5..3
%p Rows:= [seq(seq(seq(seq([w,x,y,z],z=max(y-2,0)..min(y+2,5)),y=max(x-2,0)..min(x+2,5)),x=max(w-2,0)..min(w+2,5)),w=0..5)]:
%p nrows:= nops(Rows):
%p filter:= proc(x) local i,j; add(add((x[i]-x[j])^2,i=j+1..4),j=1..3)=11 end proc:
%p T:= Matrix(nrows,nrows, proc(i,j) local k; if andmap(filter, [seq([Rows[i][k],Rows[i][k+1],Rows[j][k],Rows[j][k+1]],k=1..3)]) then 1 else 0 fi end proc):
%p U[0]:= Vector(nrows,1):
%p for j from 1 to 30 do U[j]:= T . U[j-1] od:
%p seq(add(U[n][i],i=1..nrows),n=1..30); # _Robert Israel_, Jul 30 2019
%Y Column 3 of A233818.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 16 2013
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