%I #4 Sep 20 2012 15:35:11
%S 52,1211,17336,175869,1374208,8737047,46978360,219784500,914221308,
%T 3438633452,11853180096,37855195604,113017101804,317780021548,
%U 846830343064,2150149059905,5225497612280,12203607643755,27481596234600
%N Number of side-3 hexagonal 0..n arrays with values nondecreasing E, SW and SE
%C Row 3 of A216937
%H R. H. Hardin, <a href="/A216939/b216939.txt">Table of n, a(n) for n = 1..50</a>
%F Empirical: a(n) = (1/5884534656000)*n^19 + (19/1176906931200)*n^18 + (2063/2853107712000)*n^17 + (127381/6276836966400)*n^16 + (3139187/7846046208000)*n^15 + (23993/4075868160)*n^14 + (3154906109/47076277248000)*n^13 + (437462609/724250419200)*n^12 + (2639011847/603542016000)*n^11 + (281346697/10973491200)*n^10 + (295058425993/2414168064000)*n^9 + (32651688991/68976230400)*n^8 + (158599063783/106991539200)*n^7 + (1749363777247/470762772480)*n^6 + (177682359077/24216192000)*n^5 + (26456060689/2377589760)*n^4 + (113155260151/9081072000)*n^3 + (178973011/18532800)*n^2 + (275861/60060)*n + 1
%e Some solutions for n=3
%e ......0.0.0..........0.1.2..........0.1.1..........0.0.0..........0.0.0
%e .....0.1.2.3........1.2.2.2........0.1.1.3........0.0.0.0........0.0.0.3
%e ....0.1.2.3.3......2.2.2.2.2......1.1.2.3.3......0.0.1.1.3......1.1.2.3.3
%e .....2.2.3.3........2.2.2.3........1.3.3.3........1.1.1.3........1.2.3.3
%e ......2.3.3..........2.3.3..........3.3.3..........3.3.3..........2.3.3
%K nonn
%O 1,1
%A _R. H. Hardin_ Sep 20 2012
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