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%I #5 Mar 31 2012 12:36:52
%S 1,56,8012,1441046,220242352,23491810780,1652619440763,78726503296249,
%T 2676714904101546,68406213820923245,1372665197556998950,
%U 22404250321871437486,305972684815258861606,3577152215707010961753
%N Number of nX6 nonnegative integer arrays with each row and column increasing from zero by 0, 1, 2 or 3
%C Column 6 of A202924
%H R. H. Hardin, <a href="/A202922/b202922.txt">Table of n, a(n) for n = 1..210</a>
%F Empirical: a(n) = (450901473511116613/1196222208654801945619631614956577150643837337600000000)*n^45 + (8684371008377726437/88609052492948292268120860367153863010654617600000000)*n^44 + (321356050256576651857/25892255598588786701723628029363141788827648000000000)*n^43 + (73523438668115807867/72051595782198969156058595192026234355712000000000)*n^42 + (2630205120595062219619/43010391359782037710504365497280966426624000000000)*n^41 + (88319689517641885033/31082486980872294641737572175090129305600000000)*n^40 + (32787266341330352956837883/308415977067705343582641059907331808034816000000000)*n^39 + (5770134933222248740511329/1757355994687779735513624272976249618432000000000)*n^38 + (5063895307070196088007671/59459413354097810600085031792429498368000000000)*n^37 + (501977605040256715483/267357770698196383035824202307338240000000)*n^36 + (313545922002632134008905429/8838561444528052927039666888063844352000000000)*n^35 + (54023491573302362158973153/93529750735746591820525575535067136000000000)*n^34 + (52454124636932428377298927207/6451677204160851468133232781928955904000000000)*n^33 + (233747721905718662665752653/2360009951224819924328571662342553600000000)*n^32 + (23747411771287974534439706159/22757238815382192127454083886874624000000000)*n^31 + (7498897728463553937449347123/790574053139828014353243608973312000000000)*n^30 + (16650475647977783110618061245301/224635970242159702935514505463988224000000000)*n^29 + (904048673691677542897358453/1821532731189845348055014336102400000000)*n^28 + (1057806325331348139911078162427029/370881732937745054363877052469508833280000000)*n^27 + (13760397261730470267789235303511/960584648893408584211025776921804800000000)*n^26 + (2484544479365377967720507929300981/37359881523032926721635966823851622400000000)*n^25 + (36488110994766420228523432270018759/116230742516102438689534119007538380800000000)*n^24 + (53696394537069012604625268143992489/33963528657302660656032697112592384000000000)*n^23 + (2816408843534913086886127591874273/359402419653996409058547059392512000000000)*n^22 + (314360115233264036580608523260470364873/9272043323443626359096926311737720832000000000)*n^21 + (246130204288400495078185298167342801/2020053011643491581502598324997324800000000)*n^20 + (330466598097018917704590453557735527/829935850648373286707565906886656000000000)*n^19 + (128120868347668370408791242301006609/86894992909765579163826344951808000000000)*n^18 + (7488854011004823069215993299339216849/1238801306482498361776734405132288000000000)*n^17 + (241358786375886671821070632653617/11917280485642119882412067389440000000)*n^16 + (104753894300178117952559670732725607225851/2217764038930292692170798768788078592000000000)*n^15 + (230794094447266509658278154785203352583/2106138688442823069487938052030464000000000)*n^14 + (930513963306953540221980587024421020551/2092462463193194348257496895848448000000000)*n^13 + (226265191242193621495210868239537927763/162747080470581782642249758565990400000000)*n^12 + (81897961410102872375267473968311825377/58123957310922065229374913773568000000000)*n^11 + (83416376346009382556810961685987111/57662656062422683759300509696000000000)*n^10 + (826399344631565730535305286564290457761401/25821971673969564436936120547475456000000000)*n^9 + (260099940675287786152129954306656299447/2988654128931662550571310248550400000000)*n^8 - (539435198498645811372476148725854057343/5123407078168564372407960426086400000000)*n^7 - (112564179731491559480390184291575041/348327987054972325241411450880000000)*n^6 + (346564046741548851266170979271715695919/641849053403895147765552820045824000000)*n^5 + (192682263287505752718620048904521/176264363542564713507319388160000)*n^4 - (126082847480584628412637765312129/395100513301488400929916673280000)*n^3 - (394689769881608822087888059/1096405020816651129231648000)*n^2 + (1651003017387983687/4709794079401210800)*n
%e Some solutions for n=3
%e ..0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0....0..0..0..0..0..0
%e ..0..1..1..2..2..2....0..1..1..1..1..3....0..0..1..1..1..2....0..0..1..2..2..3
%e ..0..2..2..4..4..4....0..2..2..2..2..4....0..3..3..4..4..4....0..2..2..2..4..5
%K nonn
%O 1,2
%A _R. H. Hardin_ Dec 26 2011
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