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%I #4 Dec 01 2012 07:48:03
%S 10,10,64,234,819,2563,7877,24318,74901,225552,655360,1830548,4926005,
%T 12823832,32424013,79868808,192101716,451939391,1041473168,2353902067,
%U 5224026485,11396161606,24460392989,51700266645,107691405332
%N Number of nX4 arrays of the minimum value of corresponding elements and their horizontal, vertical, diagonal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array
%C Column 4 of A219915
%H R. H. Hardin, <a href="/A219911/b219911.txt">Table of n, a(n) for n = 1..121</a>
%F Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 - (1/21777738900836704321536000000)*n^28 + (61/6222211114524772663296000000)*n^27 - (43/31425308659216023552000000)*n^26 + (17/125132450769728962560000)*n^25 - (28109/2863608007999566643200000)*n^24 + (790000019/1563529972367763387187200000)*n^23 - (7238713/441425740363569561600000)*n^22 + (110073307/882851480727139123200000)*n^21 + (4489349/230992014842265600000)*n^20 - (543475622663/462446013714215731200000)*n^19 + (2560006651583/85187423578934476800000)*n^18 + (2310801616411997/46512333274098224332800000)*n^17 - (589559743689019/17766361067264409600000)*n^16 + (496003326175726703/390859943479817011200000)*n^15 - (209411840851547611/9306189130471833600000)*n^14 + (8651366663182657/468062766917222400000)*n^13 + (88016360529632233/9308066387558400000)*n^12 - (26031638075762884878329/105340233495851827200000)*n^11 + (120380686054081150949947/41383663159084646400000)*n^10 - (366096865860529707276691/133888321985273856000000)*n^9 - (27222349343899273729289/57898389136896000000)*n^8 + (4251094114198631270606723/540988073497872000000)*n^7 - (148882500240267881827577429/2448107645727744000000)*n^6 + (17631394572311382143692779449/122527787668673587200000)*n^5 + (465421984465716632128098689/291732827782556160000)*n^4 - (241713358053685840278268817/14586641389127808000)*n^3 + (706593057831502942631/10962783631800)*n^2 - (8901027387557259947/93163582512)*n - 5119093 for n>18
%e Some solutions for n=3
%e ..2..1..1..1....0..0..0..0....2..2..2..2....1..0..0..0....2..1..0..0
%e ..2..1..0..0....0..0..0..0....2..2..2..2....1..0..0..0....2..1..0..0
%e ..2..1..0..0....2..2..2..2....2..2..2..2....1..1..1..2....2..2..0..0
%K nonn
%O 1,1
%A _R. H. Hardin_ Dec 01 2012
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