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%I #4 Dec 07 2012 07:04:05
%S 10,36,238,1013,3916,15067,58288,218422,773169,2583728,8224585,
%T 25167752,74507806,214204816,599356409,1634563737,4349942989,
%U 11308092511,28744810615,71518831786,174334969663,416723727408,977666680868
%N Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array
%C Column 3 of A220204
%H R. H. Hardin, <a href="/A220199/b220199.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/552610124608731372158976000000)*n^29 - (1/38111043076464232562688000000)*n^28 - (43/10888869450418352160768000000)*n^27 + (1013/1209874383379816906752000000)*n^26 - (37/969450627708186624000000)*n^25 + (59/846066002363508326400000)*n^24 + (54830099/390882493091940846796800000)*n^23 - (7939573/894467947578812006400000)*n^22 + (5134253/22071287018178478080000)*n^21 + (37966001/9196369590907699200000)*n^20 - (152257814897/269760174666625843200000)*n^19 + (918505603831/42593711789467238400000)*n^18 - (962278931784007/2907020829631139020800000)*n^17 - (1930456964404139/342002450544839884800000)*n^16 + (43256823284606443/97714985869954252800000)*n^15 - (33779034291676489/2961060177877401600000)*n^14 + (990119936607349039/7098951964911206400000)*n^13 + (8261472616915478693/21296855894733619200000)*n^12 - (14609050016004250375909/289685642113592524800000)*n^11 + (606095725965810479424827/579371284227185049600000)*n^10 - (6894383399300066098456333/569025368437413888000000)*n^9 + (3094992352284156140975351/42150027291660288000000)*n^8 + (7175705615099463540165439/60590664231761664000000)*n^7 - (204006830067393368414683721/26929184103005184000000)*n^6 + (51776746394532001962514261613/612638938343367936000000)*n^5 - (1063830518327474508898879/1954191190887936000)*n^4 + (31834015971911914244845247/14586641389127808000)*n^3 - (480939292908953611199/96472495959840)*n^2 + (10194642893164011521/2329089562800)*n + 2343378 for n>10
%e Some solutions for n=3
%e ..3..0..0....1..1..1....2..1..1....1..0..0....2..2..2....0..0..0....1..1..1
%e ..3..1..0....1..1..1....2..1..1....3..1..0....2..0..0....2..0..0....2..1..1
%e ..3..3..1....3..2..1....3..1..1....3..1..1....3..0..0....3..1..1....3..3..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Dec 07 2012
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