%I #4 Dec 03 2012 09:46:10

%S 10,25,184,927,4415,19083,79295,321566,1259568,4717825,16857776,

%T 57606698,189020066,597912638,1829586732,5430748522,15671204978,

%U 44036228316,120655436611,322669774355,842965290520,2152858503411,5378480168433

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

%C Column 3 of A220044

%H R. H. Hardin, <a href="/A220039/b220039.txt">Table of n, a(n) for n = 1..210</a>

%F Empirical: a(n) = (1/1473626998956616992423936000000)*n^29 + (29/152444172305856930250752000000)*n^28 + (59/3111105557262386331648000000)*n^27 + (2017/2419748766759633813504000000)*n^26 + (601/26590645788567404544000000)*n^25 + (31699/37226904103994366361600000)*n^24 + (2405969/86862776242653521510400000)*n^23 + (33596467/33989782007994856243200000)*n^22 + (8427299/441425740363569561600000)*n^21 - (56013571/147141913454523187200000)*n^20 + (7573675663/231223006857107865600000)*n^19 + (4835290079/85187423578934476800000)*n^18 - (147414520045721/7752055545683037388800000)*n^17 + (1259847810695701/1368009802179359539200000)*n^16 - (3534942904775483/195429971739908505600000)*n^15 + (7586986411861739/65143323913302835200000)*n^14 + (35875362222238793/6084815969923891200000)*n^13 - (2023861913558150999/10648427947366809600000)*n^12 + (949264631277979465741/386247522818123366400000)*n^11 - (158674084376846602013/18105352632099532800000)*n^10 - (29086073964564053405867/2276101473749655552000000)*n^9 - (100284692080335198298013/21075013645830144000000)*n^8 + (10249261275490896843093097/69246473407727616000000)*n^7 - (57286214031737857091569957/26929184103005184000000)*n^6 + (11416083601292776555849018201/612638938343367936000000)*n^5 - (224722631042592670823040637/2042129794477893120000)*n^4 + (6939398231304078884944021/14586641389127808000)*n^3 - (3136625071649948281553/1929449919196800)*n^2 + (55228499034291227/13233463425)*n - 5647472 for n>9

%e Some solutions for n=3

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

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

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

%K nonn

%O 1,1

%A _R. H. Hardin_ Dec 03 2012