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%I #8 Aug 30 2018 06:07:29
%S 64,1000,6094,27790,102232,319769,881519,2196522,5038720,10788462,
%T 21789398,41858498,76994510,136338455,233448747,387963222,627730762,
%U 991506308,1532314870,2321602662,3454306716,5054988261,7285189791
%N Number of 3 X n 0..3 arrays with diagonals and antidiagonals unimodal and rows nondecreasing.
%C Row 3 of A224391.
%H R. H. Hardin, <a href="/A224392/b224392.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (353/181440)*n^9 + (17/560)*n^8 + (9731/30240)*n^7 + (1283/720)*n^6 + (52457/8640)*n^5 + (776/45)*n^4 + (294499/11340)*n^3 + (28837/2520)*n^2 + (8207/126)*n - 18 for n>1.
%F Conjectures from _Colin Barker_, Aug 30 2018: (Start)
%F G.f.: x*(64 + 360*x - 1026*x^2 + 4170*x^3 - 7998*x^4 + 10591*x^5 - 9351*x^6 + 5629*x^7 - 2165*x^8 + 478*x^9 - 46*x^10) / (1 - x)^10.
%F a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>11.
%F (End)
%e Some solutions for n=3:
%e ..0..1..1....0..1..1....1..1..2....0..0..1....0..1..1....1..1..3....0..2..2
%e ..2..2..2....0..0..1....2..3..3....2..2..2....2..2..2....1..2..3....1..2..3
%e ..0..2..2....0..0..0....1..1..2....1..3..3....0..0..1....1..3..3....0..3..3
%Y Cf. A224391.
%K nonn
%O 1,1
%A _R. H. Hardin_, Apr 05 2013
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