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%I #4 Nov 28 2012 17:44:00
%S 20,60,394,2106,9920,45471,186016,724385,2669247,9382490,31608418,
%T 102225635,318518736,959098084,2798488049,7930889244,21872282847,
%U 58800825814,154339095726,396109474270,995411502191,2452409070582
%N Number of 3Xn 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 columns, 0..3 3Xn array
%C Row 3 of A219828
%H R. H. Hardin, <a href="/A219830/b219830.txt">Table of n, a(n) for n = 1..122</a>
%F Empirical: a(n) = (1/523022617466601111760007224100074291200000000)*n^38 - (1/2117500475573283853279381474089369600000000)*n^37 + (1/14587973599603969312470566594150400000000)*n^36 - (83/35427935884752496901714233157222400000000)*n^35 - (14227/17713967942376248450857116578611200000000)*n^34 + (92611/520999057128713189731091664076800000000)*n^33 - (718793/43244981026493980175308003737600000000)*n^32 + (421750447/994634563609361544032084085964800000000)*n^31 + (4066067/41695888138898805006689894400000000)*n^30 - (14899737877/1018570981678813665163424563200000000)*n^29 + (362803671817/386354510291963804027505868800000000)*n^28 - (4454639052301/386354510291963804027505868800000000)*n^27 - (1649876745871/487586821882887012294328320000000)*n^26 + (20519202128355611/62411113201009537573674024960000000)*n^25 - (3696580966990558379/270448157204374662819254108160000000)*n^24 + (32891015046758353/2272673589952728258985328640000000)*n^23 + (334530395892109581739/10384231897175311728802529280000000)*n^22 - (19993072986873931454773/10384231897175311728802529280000000)*n^21 + (35522994168079491352164427/731172092995226361139801620480000000)*n^20 + (231274940235499832643847507/654206609522044638914559344640000000)*n^19 - (437293316775378726130512266011/5996893920618742523383460659200000000)*n^18 + (2046644984310601097652571037/787407289997208839729971200000000)*n^17 - (5309867465218873387186304463367/144882941359486426510314700800000000)*n^16 - (35138439129467275794678974801347/72441470679743213255157350400000000)*n^15 + (25378033018766527750851314092401607/760635442137303739179152179200000000)*n^14 - (2413503388657823473619412417861673/3656901164121652592207462400000000)*n^13 + (389927473209173258299840076447069/101094556371252490587340800000000)*n^12 + (26949758648166352764552439627837271/274399510150542474451353600000000)*n^11 - (143682181985388259279429358505549379/57663665176563273616588800000000)*n^10 + (1165481026975278114574930222502197841/55261012460873137215897600000000)*n^9 + (153317430943805345023134433901045273801/4885482842374228834605465600000000)*n^8 - (51309107540611070803697805141593130811/26942000968975526661427200000000)*n^7 + (142189296545753805719156272015318528303/17302751733408727122561024000000)*n^6 + (6785882934464320230463825994872500533/88279345578615954706944000000)*n^5 - (259839864146482678319532831539837941/484670916902205241528320000)*n^4 - (112008442781460076632482023553492423/24522040438504431863040000)*n^3 + (6921128901259162646846660417389/119653169003778009600)*n^2 - (1035810921543168836863210769/5342931457063200)*n + 155842923606 for n>31
%e Some solutions for n=3
%e ..0..0..2....1..0..2....1..1..3....1..1..2....0..0..2....0..0..1....0..0..0
%e ..2..0..1....2..0..0....2..1..2....1..1..2....0..0..1....1..0..0....0..0..0
%e ..3..1..1....3..0..2....2..2..2....1..1..1....0..0..3....1..0..3....1..1..3
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 28 2012
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