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A207110 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.

%I A207110 #11 Jul 22 2025 20:01:44
%S A207110 25,625,3399,11511,30415,68737,139341,260597,457869,765241,1227499,
%T A207110 1902387,2863155,4201417,6030337,8488161,11742113,15992673,21478255,
%U A207110 28480303,37328823,48408369,62164501,79110733,99835989,125012585
%N A207110 Number of n X 7 0..1 arrays avoiding 0 0 0 and 0 1 1 horizontally and 0 0 1 and 1 1 0 vertically.
%C A207110 Column 7 of A207111.
%H A207110 R. H. Hardin, <a href="/A207110/b207110.txt">Table of n, a(n) for n = 1..210</a>
%F A207110 Empirical: a(n) = (1/280)*n^7 + (7/45)*n^6 + (47/15)*n^5 + (206/9)*n^4 + (4111/120)*n^3 - (1037/45)*n^2 - (4493/210)*n + 9.
%F A207110 Conjectures from _Colin Barker_, Jun 19 2018: (Start)
%F A207110 G.f.: x*(25 + 425*x - 901*x^2 + 419*x^3 + 249*x^4 - 269*x^5 + 79*x^6 - 9*x^7) / (1 - x)^8.
%F A207110 a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8) for n>8.
%F A207110 (End)
%e A207110 Some solutions for n=4:
%e A207110 ..1..1..1..0..0..1..0....0..1..0..0..1..0..1....0..0..1..0..0..1..0
%e A207110 ..0..1..0..1..0..0..1....1..0..0..1..0..0..1....1..1..1..0..0..1..0
%e A207110 ..1..1..0..1..0..1..0....1..1..0..1..0..0..1....0..0..1..0..0..1..0
%e A207110 ..1..1..0..1..0..0..1....1..0..0..1..0..0..1....1..0..1..0..0..1..0
%Y A207110 Cf. A207111.
%K A207110 nonn
%O A207110 1,1
%A A207110 _R. H. Hardin_, Feb 15 2012