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A251270 Number of (3+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.

%I A251270 #7 Nov 27 2018 11:58:40
%S A251270 108,480,1667,4930,13052,31936,73805,163604,351804,740008,1532159,
%T A251270 3136950,6372636,12876648,25924809,52069752,104417740,209182288,
%U A251270 418791387,838101930,1676828540,3354401200,6709680485,13420387996
%N A251270 Number of (3+1) X (n+1) 0..1 arrays with no 2 X 2 subblock having x11-x00 less than x10-x01.
%H A251270 R. H. Hardin, <a href="/A251270/b251270.txt">Table of n, a(n) for n = 1..210</a>
%F A251270 Empirical: a(n) = 9*a(n-1) - 35*a(n-2) + 77*a(n-3) - 105*a(n-4) + 91*a(n-5) - 49*a(n-6) + 15*a(n-7) - 2*a(n-8).
%F A251270 Conjectures from _Colin Barker_, Nov 27 2018: (Start)
%F A251270 G.f.: x*(108 - 492*x + 1127*x^2 - 1589*x^3 + 1407*x^4 - 769*x^5 + 238*x^6 - 32*x^7) / ((1 - x)^7*(1 - 2*x)).
%F A251270 a(n) = (5760*(25*2^(1 + n)-49) - 186828*n - 57236*n^2 - 9885*n^3 - 905*n^4 - 27*n^5 + n^6) / 360.
%F A251270 (End)
%e A251270 Some solutions for n=4:
%e A251270 ..0..0..0..1..1....0..0..1..0..1....0..0..1..0..1....0..1..0..1..1
%e A251270 ..0..0..0..1..1....1..1..0..1..0....0..0..0..1..1....0..0..1..1..1
%e A251270 ..0..0..0..1..1....0..0..1..0..1....0..1..1..1..1....0..0..0..1..1
%e A251270 ..0..0..1..1..1....1..1..0..1..1....0..0..0..0..0....0..0..0..0..0
%Y A251270 Row 3 of A251268.
%K A251270 nonn
%O A251270 1,1
%A A251270 _R. H. Hardin_, Dec 01 2014