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A207303 Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207303 #12 Oct 26 2024 03:31:59
%S A207303 19,361,1675,4939,11497,23091,41893,70537,112151,170389,249463,354175,
%T A207303 489949,662863,879681,1147885,1475707,1872161,2347075,2911123,3575857,
%U A207303 4353739,5258173,6303537,7505215,8879629,10444271,12217735,14219749
%N A207303 Number of n X 6 0..1 arrays avoiding 0 0 0 and 1 0 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207303 Column 6 of A207305.
%H A207303 R. H. Hardin, <a href="/A207303/b207303.txt">Table of n, a(n) for n = 1..210</a>
%F A207303 Empirical: a(n) = (4/15)*n^5 + (45/4)*n^4 + (199/6)*n^3 - (73/4)*n^2 - (373/30)*n + 5.
%F A207303 Conjectures from _Colin Barker_, Jun 21 2018: (Start)
%F A207303 G.f.: x*(19 + 247*x - 206*x^2 - 76*x^3 + 53*x^4 - 5*x^5) / (1 - x)^6.
%F A207303 a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>6. (End)
%e A207303 Some solutions for n=4:
%e A207303 ..1..0..0..1..0..0....1..1..0..0..1..1....0..0..1..0..0..1....0..0..1..0..0..1
%e A207303 ..0..1..0..0..1..0....1..1..1..1..0..0....1..0..0..1..1..0....0..1..1..0..0..1
%e A207303 ..1..1..0..0..1..0....1..1..0..0..1..1....1..0..0..1..0..0....0..1..1..0..0..1
%e A207303 ..1..1..0..0..1..0....1..1..1..0..0..1....1..0..0..1..1..0....0..1..1..0..0..1
%Y A207303 Cf. A207305.
%K A207303 nonn
%O A207303 1,1
%A A207303 _R. H. Hardin_, Feb 16 2012