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%I #4 Nov 17 2012 07:01:29
%S 10,35,261,1540,8424,42938,204842,912956,3824676,15209685,57837351,
%T 211203417,742716089,2521452690,8283479640,26391360139,81707036845,
%U 246254219675,723671248714,2076719332039,5827511255940,16010189488131
%N Number of nX4 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 columns, 0..2 nX4 array
%C Column 4 of A219299
%H R. H. Hardin, <a href="/A219295/b219295.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (1/2068985932089345445143714841228895839753581059112960000000000)*n^48 - (1/2938900471717820234579140399472863408740882186240000000000)*n^47 + (263/2201048863924835579940122171520101957184660701184000000000)*n^46 - (6007/239244441730960389123926322991315430128767467520000000000)*n^45 + (50069/16789083630242834324486057753776521412545085440000000000)*n^44 - (8447/219691865684995765954018662067323627299143680000000000)*n^43 - (2425729/40464176191282941078042507059841933214167859200000000)*n^42 + (6456461251/505802202391036763475531338248024165177098240000000000)*n^41 - (7910589569/5805477215392100585085008186490951680655360000000000)*n^40 + (635714792519/12336639082708213743305642396293272321392640000000000)*n^39 + (2934583768583/347956486948180387631697606049297424449536000000000)*n^38 - (258513228301/146040664378485850596700078086668943360000000000)*n^37 + (62735759945677211/386068363896985351853092649670628721295360000000000)*n^36 - (605190193476760471/96517090974246337963273162417657180323840000000000)*n^35 - (16195260707344914389/38606836389698535185309264967062872129536000000000)*n^34 + (45002523646996250213/516134176332868117450658622554316472320000000000)*n^33 - (107357996308456700568959/15598721773615569771842127259419342274560000000000)*n^32 + (245574524125267202856061/974920110850973110740132953713708892160000000000)*n^31 + (29329920367189350322176787/4302228102077842630620973808646302466048000000000)*n^30 - (17233754440279187907948833777/10755570255194606576552434521615756165120000000000)*n^29 + (78809243143524283334867301991/709512880402642712696112622115582115840000000000)*n^28 - (1431685429549914195126529812853/370881732937745054363877052469508833280000000000)*n^27 - (780855952559105537910112194487/50652134107017273281544342388548304896000000000)*n^26 + (8396578412219026295997026753964457/801992123361106826957785421152014827520000000000)*n^25 - (29427927770904147251879518763484131341/44156742792117411178381597305781522268160000000000)*n^24 + (357909666573191544973210530241590019/16125292736423698015820741411717775360000000000)*n^23 - (3124345745687984741443860801931745549/14835269317509802174555082098780353331200000000)*n^22 - (1899813052581924621298726538252632595593/92720433234436263590969263117377208320000000000)*n^21 + (2400133175657230776205423624630996989769483/1792595042532434429425405753602626027520000000000)*n^20 - (84666284316835179544598578672853761913291/1965564739618897400685751922809896960000000000)*n^19 + (13155293627015393737578237426652247275438799/18850994330907487883451789534698668032000000000)*n^18 + (44916063205741479447447610265518127388127633/8064596505201064335166540977411194880000000000)*n^17 - (4310739889918667105115476673383375496587807831149/6032318185890396122704572651103573770240000000000)*n^16 + (17412795737823621370316781189863331576398014086107/754039773236299515338071581387946721280000000000)*n^15 - (549600365180627248402441756438789486402367877163/1288956877327007718526618087842643968000000000)*n^14 + (521866482793895060053248784040022673823996026951/146472372423523604378024782709391360000000000)*n^13 + (4848121820209457205581557002704896843599370569771631/99156371228043127437834702902305751040000000000)*n^12 - (21698322350505467868276788384809961291385524241574661/9295909802629043197297003397091164160000000000)*n^11 + (6065237087365322957226008597625910317137670951433787/137717182261171010330325976253202432000000000)*n^10 - (32123316780570726685751559278978549210460519755297281/64554929184923911092340301368688640000000000)*n^9 + (11431514683849398552329667271018101135613795626527051/4006091924650936897508837415518208000000000)*n^8 + (665617182234829594631360951601855459267454356632141/66837174156108089767322029194854400000000)*n^7 - (29337384713005817938329570008353502184994321542678083/74665339159255049073403439162818560000000)*n^6 + (7255725517914961148014609680320925834651869548590583/1724969331022968209619923203873152000000)*n^5 - (6452409382577447522445298069183521345083842965947111/251900283260496944896877674216396800000)*n^4 + (802069683807706591807466239455085712074440024649/9087311805934233221388083485440000)*n^3 - (1856000937386895291592995047238075803336459/16576417167871326862928832000)*n^2 - (21969573307337394728413497909582977/88544128692742763040)*n + 762873671064076 for n>25
%e Some solutions for n=3
%e ..0..0..0..1....0..0..0..1....0..0..0..1....0..0..0..0....0..0..0..0
%e ..0..0..1..1....0..0..1..1....0..0..0..2....0..0..0..2....0..0..0..1
%e ..2..2..2..2....0..1..1..1....0..0..1..2....0..0..0..2....1..2..1..1
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 17 2012
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