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%I #8 Nov 24 2018 08:13:13
%S 854,4334,10289,24893,53306,114512,237143,498593,1050871,2263156,
%T 4941211,10973705,24635963,55831811,127245743,291219638,668084936,
%U 1535123866,3530526046,8124227554,18700618529,43053766658,99130762082,228260731322
%N Number of (n+1) X (3+1) 0..3 arrays with no 2 X 2 subblock having the sum of its diagonal elements greater than the absolute difference of its antidiagonal elements.
%H R. H. Hardin, <a href="/A251050/b251050.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 8*a(n-1) - 25*a(n-2) + 35*a(n-3) - 7*a(n-4) - 49*a(n-5) + 77*a(n-6) - 55*a(n-7) + 20*a(n-8) - 3*a(n-9) for n>12.
%F Empirical g.f.: x*(854 - 2498*x - 3033*x^2 + 21041*x^3 - 34325*x^4 + 22458*x^5 + 1073*x^6 - 9797*x^7 + 4718*x^8 - 398*x^9 - 153*x^10 + 3*x^11) / ((1 - x)^7*(1 - x - 3*x^2)). - _Colin Barker_, Nov 24 2018
%e Some solutions for n=4:
%e ..0..1..1..3....0..2..3..3....0..1..2..3....0..0..0..3....0..2..2..2
%e ..1..0..0..0....0..0..0..0....0..0..0..0....0..0..0..3....0..0..0..0
%e ..1..0..0..0....2..2..2..2....1..0..0..0....2..0..0..2....0..0..0..0
%e ..1..0..0..0....0..0..0..0....2..0..0..0....2..0..0..1....1..0..0..0
%e ..3..0..0..0....1..1..1..1....3..1..1..0....3..0..0..1....3..2..2..0
%Y Column 3 of A251055.
%K nonn
%O 1,1
%A _R. H. Hardin_, Nov 29 2014
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