%I #12 Dec 30 2023 23:11:31
%S 3496,11622,38220,150572,578992,2642176,11510748,59677576,286598096,
%T 1625122820,8327165492,49678143548,264612547304,1617434567048,
%U 8813023956528,54391352548384,300504986392076,1859027129125504
%N Number of (n+1) X (3+1) 0..6 arrays with every 2 X 2 subblock having the sum of the absolute values of all six edge and diagonal differences equal to 18.
%C Column 3 of A233997.
%H R. H. Hardin, <a href="/A233992/b233992.txt">Table of n, a(n) for n = 1..210</a>
%H Robert Israel, <a href="/A233992/a233992_1.txt">Linear recurrence of order 292</a>.
%e Some solutions for n=4:
%e 0 5 0 2 3 6 3 0 4 1 3 6 4 1 1 4 2 5 0 3
%e 5 6 5 5 6 1 6 3 1 6 6 1 1 6 0 5 1 6 5 0
%e 0 5 0 6 3 6 3 0 6 3 1 4 6 3 3 0 1 0 5 2
%e 1 4 1 1 0 3 0 5 1 6 6 1 1 6 0 5 1 6 5 0
%e 6 1 6 0 3 6 3 0 3 6 0 1 2 5 5 6 1 0 5 2
%p good:=select(proc(t) local i,j; add(add(abs(t[i]-t[j]),j=i+1..4),i=1..3)=18 end proc, [seq(seq(seq(seq([a,b,c,d],a=0..6),b=0..6),c=0..6),d=0..6)]):
%p good2:= convert(map(t -> t[1..2], good), set):
%p configs:= select(t -> member([t[1][2],t[2][1]], good2),
%p {seq(seq([t1,t2],t1=good2),t2=good2)]:
%p N:= nops(configs):
%p T:= Matrix(N,N, proc(i,j) local k; if
%p {seq([op(configs[i][k..k+1]),op(configs[j][k..k+1])],k=1..3)} subset good then 1 else 0 fi end proc):
%p e:= Vector(N,1):
%p u[0]:= e:
%p for i from 1 to 30 do
%p u[i]:= T . u[i-1]
%p od:
%p seq(e^%T . u[i], i=1..30); # _Robert Israel_, Dec 25 2023
%Y Cf. A233997.
%K nonn
%O 1,1
%A _R. H. Hardin_, Dec 18 2013