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A207066 Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.

%I A207066 #9 Jun 18 2018 14:17:51
%S A207066 21,441,2499,8799,23856,54684,111426,208026,362943,599907,948717,
%T A207066 1446081,2136498,3073182,4319028,5947620,8044281,10707165,14048391,
%U A207066 18195219,23291268,29497776,36994902,45983070,56684355,69343911,84231441
%N A207066 Number of n X 6 0..1 arrays avoiding 0 0 1 and 0 1 0 horizontally and 0 0 1 and 1 0 1 vertically.
%C A207066 Column 6 of A207068.
%H A207066 R. H. Hardin, <a href="/A207066/b207066.txt">Table of n, a(n) for n = 1..210</a>
%F A207066 Empirical: a(n) = (7/120)*n^6 + (147/40)*n^5 + (49/3)*n^4 + (91/8)*n^3 - (707/120)*n^2 - (91/20)*n.
%F A207066 Conjectures from _Colin Barker_, Jun 18 2018: (Start)
%F A207066 G.f.: 21*x*(1 + 14*x - 7*x^2 - 8*x^3 + 2*x^4) / (1 - x)^7.
%F A207066 a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>7.
%F A207066 (End)
%e A207066 Some solutions for n=4:
%e A207066 ..0..0..0..0..0..0....0..1..1..1..0..0....1..0..1..1..1..0....1..1..1..1..1..0
%e A207066 ..1..0..1..1..1..0....1..0..1..1..1..0....0..1..1..1..1..0....0..0..0..0..0..0
%e A207066 ..0..0..0..0..0..0....1..0..0..0..0..0....0..1..1..1..0..0....0..0..0..0..0..0
%e A207066 ..0..0..0..0..0..0....1..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%Y A207066 Cf. A207068.
%K A207066 nonn
%O A207066 1,1
%A A207066 _R. H. Hardin_, Feb 14 2012