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%I #4 Nov 03 2013 07:46:55
%S 8,42,139,748,2379,13785,43004,253150,793041,4669709,14671984,
%T 86434175,271693559,1601479258,5034665244,29682509736,93325900298,
%U 550249461287,1730155635975,10201324308311,32076766175871,189133666816468
%N Number of black square subarrays of (n+1)X(6+1) binary arrays with no element equal to a strict majority of its diagonal and antidiagonal neighbors, with upper left element zero
%C Column 6 of A231070
%H R. H. Hardin, <a href="/A231069/b231069.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 46*a(n-2) -873*a(n-4) +10049*a(n-6) -84447*a(n-8) +562572*a(n-10) -3067159*a(n-12) +13891260*a(n-14) -52935814*a(n-16) +172217299*a(n-18) -484689977*a(n-20) +1190134475*a(n-22) -2558652242*a(n-24) +4820557844*a(n-26) -7965409977*a(n-28) +11572562962*a(n-30) -14858863618*a(n-32) +16991999037*a(n-34) -17461801546*a(n-36) +16238944429*a(n-38) -13686724101*a(n-40) +10397239696*a(n-42) -7043263035*a(n-44) +4203452626*a(n-46) -2187172255*a(n-48) +984805610*a(n-50) -381851657*a(n-52) +127072644*a(n-54) -36179358*a(n-56) +8775147*a(n-58) -1797418*a(n-60) +304631*a(n-62) -40963*a(n-64) +4058*a(n-66) -260*a(n-68) +8*a(n-70)
%e Some solutions for n=4
%e ..x..0..x..0..x..1..x....x..0..x..1..x..1..x....x..0..x..0..x..1..x
%e ..1..x..1..x..1..x..0....1..x..0..x..0..x..0....1..x..1..x..1..x..0
%e ..x..0..x..0..x..1..x....x..1..x..1..x..1..x....x..0..x..0..x..0..x
%e ..0..x..1..x..0..x..0....0..x..1..x..0..x..1....0..x..0..x..0..x..1
%e ..x..1..x..0..x..1..x....x..0..x..0..x..0..x....x..1..x..1..x..1..x
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 03 2013
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