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%I #9 Dec 15 2018 14:21:23
%S 8501,9679,11937,18526,32652,63550,133284,296566,694572,1704910,
%T 4368564,11624806,31924092,89883070,257882244,750124246,2203339212,
%U 6515962030,19359786324,57703170886,172357147932,515566725790,1543690752804
%N Number of (n+1) X (5+1) 0..2 arrays with every 2 X 2 subblock diagonal minus antidiagonal sum nondecreasing horizontally, vertically and ne-to-sw antidiagonally.
%H R. H. Hardin, <a href="/A253492/b253492.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = 6*a(n-1) - 11*a(n-2) + 6*a(n-3) for n>6.
%F Empirical: a(n) = 49*3^(n-1) + 1435*2^(n-1) + 5723 for n>3.
%F Conjectures from _Colin Barker_, Dec 15 2018: (Start)
%F G.f.: x*(8501 - 41327*x + 47374*x^2 + 2367*x^3 - 5271*x^4 - 198*x^5) / ((1 - x)*(1 - 2*x)*(1 - 3*x)).
%F a(n) = (34338 + 4305*2^n + 98*3^n) / 6 for n>3.
%F (End)
%e Some solutions for n=4:
%e ..0..1..0..0..0..1....1..1..0..1..1..1....2..2..2..2..2..1....1..0..2..2..1..0
%e ..2..2..1..1..1..2....2..2..1..2..2..2....2..2..2..2..2..1....2..0..2..2..1..0
%e ..2..2..1..1..1..2....1..1..0..1..1..1....2..2..2..2..2..1....2..0..2..2..1..0
%e ..2..2..1..1..1..2....2..2..1..2..2..2....2..2..2..2..2..1....2..0..2..2..1..0
%e ..1..1..0..0..0..1....2..2..1..2..2..2....0..0..0..1..2..2....2..0..2..2..1..2
%Y Column 5 of A253495.
%K nonn
%O 1,1
%A _R. H. Hardin_, Jan 02 2015
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