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%I #14 May 09 2020 15:04:00
%S 16,256,2500,16900,87616,372100,1352569,4338889,12559936,33362176,
%T 82373776,190992400,419266576,877225924,1759047481,3396208729,
%U 6338070544,11471266816,20192978404,34657779556,58123423744,95427859396
%N Number of n X 2 0..3 arrays with rows, antidiagonals and columns unimodal.
%C Column 2 of A223762.
%H R. H. Hardin, <a href="/A223756/b223756.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/518400)*n^12 + (1/17280)*n^11 + (91/103680)*n^10 + (71/8640)*n^9 + (9101/172800)*n^8 + (457/1920)*n^7 + (81397/103680)*n^6 + (497/270)*n^5 + (203687/64800)*n^4 + (1933/540)*n^3 + (2533/720)*n^2 + (11/6)*n + 1.
%F a(n) = A223659(n)^2. - _Mark van Hoeij_, May 14 2013
%F Conjectures from _Colin Barker_, Feb 19 2018: (Start)
%F G.f.: x*(16 + 48*x + 420*x^2 - 208*x^3 + 1140*x^4 - 1260*x^5 + 1401*x^6 - 1044*x^7 + 597*x^8 - 244*x^9 + 69*x^10 - 12*x^11 + x^12) / (1 - x)^13.
%F a(n) = 13*a(n-1) - 78*a(n-2) + 286*a(n-3) - 715*a(n-4) + 1287*a(n-5) - 1716*a(n-6) + 1716*a(n-7) - 1287*a(n-8) + 715*a(n-9) - 286*a(n-10) + 78*a(n-11) - 13*a(n-12) + a(n-13) for n>13.
%F (End)
%e Some solutions for n=3:
%e ..3..2....0..0....0..0....1..2....0..3....2..1....1..3....0..0....3..1....3..1
%e ..2..0....1..1....1..2....3..2....1..3....2..3....3..3....0..0....1..0....2..3
%e ..2..0....3..0....1..2....0..0....2..1....1..3....3..2....0..3....1..0....0..3
%K nonn
%O 1,1
%A _R. H. Hardin_, Mar 27 2013
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