%I #4 Dec 03 2012 05:42:26

%S 10,19,109,560,2410,9094,32575,114987,396917,1315916,4156201,12519404,

%T 36142411,100533680,270678655,708009173,1804416902,4491311579,

%U 10939219139,26113766099,61178754251,140820281122,318767877586

%N Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array

%C Column 3 of A220010

%H R. H. Hardin, <a href="/A220005/b220005.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 + (1/152444172305856930250752000000)*n^28 - (1/3350421369359492972544000000)*n^27 + (1/25471039650101408563200000)*n^26 + (43/41363226782215962624000000)*n^25 - (5029/37226904103994366361600000)*n^24 + (870547/91972351315750787481600000)*n^23 - (404867/6797956401598971248640000)*n^22 - (2777213/176570296145427824640000)*n^21 + (157540321/147141913454523187200000)*n^20 - (8521847489/359680232888834457600000)*n^19 - (5896756171/17037484715786895360000)*n^18 + (1999193158206953/46512333274098224332800000)*n^17 - (1754864756699611/1368009802179359539200000)*n^16 + (347465675323531/30066149498447462400000)*n^15 + (5807854993750157/13028664782660567040000)*n^14 - (63962106808513283/3549475982455603200000)*n^13 + (726321071153298251/2662106986841702400000)*n^12 - (148797834273315164401/289685642113592524800000)*n^11 - (611073680485163068111/11587425684543700992000)*n^10 + (1108080234396388175644549/1138050736874827776000000)*n^9 - (58248175543969688527/7702855864704000000)*n^8 + (283282051354077778828369/28513253756123136000000)*n^7 + (1544529331894217156756731/5385836820601036800000)*n^6 - (1108226389277296065072353107/612638938343367936000000)*n^5 - (8742494209572335492077019/2042129794477893120000)*n^4 + (130381592817894359575/1282342100143104)*n^3 - (101179310872363022329/192944991919680)*n^2 + (2861223530470917191/2329089562800)*n - 1126080 for n>10

%e Some solutions for n=3

%e ..3..0..0....2..2..2....2..0..0....1..1..1....2..2..2....0..0..0....0..0..0

%e ..3..0..0....2..0..0....2..0..0....1..0..0....2..1..1....0..0..0....0..0..0

%e ..3..2..2....0..0..0....1..1..1....0..0..0....1..1..1....3..0..0....2..2..3

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 03 2012