|
%I #4 Nov 24 2012 08:30:57
%S 15,56,566,5072,37215,231634,1278800,6443507,30195206,133142378,
%T 557224292,2226287479,8525154062,31384203039,111360954329,
%U 381756818469,1267093120873,4079967342109,12767836083797,38896345678043
%N Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..2 4Xn array
%C Row 4 of A219627
%H R. H. Hardin, <a href="/A219630/b219630.txt">Table of n, a(n) for n = 1..145</a>
%F Empirical: a(n) = (1/775869724533504541928893065460835939907592897167360000000000)*n^48 - (1/4040988148612002822546318049275187187018713006080000000000)*n^47 - (521/16507866479436266849550916286400764678884955258880000000000)*n^46 + (6143/239244441730960389123926322991315430128767467520000000000)*n^45 - (64489/14073202454762375830819195470077378242868674560000000000)*n^44 + (130909/2416610522534953425494205282740559900290580480000000000)*n^43 + (215508281/1517406607173110290426594014744072495531294720000000000)*n^42 - (15865561379/505802202391036763475531338248024165177098240000000000)*n^41 + (1593442699/544263488943009429851719517483526720061440000000000)*n^40 + (1023347049017/12336639082708213743305642396293272321392640000000000)*n^39 - (87480389842147/1304836826055676453618866022684865341685760000000000)*n^38 + (11780375682203/1130462920559390473137419122967178117120000000000)*n^37 - (241748764071914483/289551272922739013889819487252971540971520000000000)*n^36 + (1041961583157709727/96517090974246337963273162417657180323840000000000)*n^35 + (116295075190994577853/17032427818984647875871734544292443586560000000000)*n^34 - (29004471344154799303/27164956649098321971087295923911393280000000000)*n^33 + (537711438361496467283671/5849520665105838664440797722282253352960000000000)*n^32 - (4555770374748739500515537/974920110850973110740132953713708892160000000000)*n^31 + (1327489994831180757583537043/32266710765583819729657303564847268495360000000000)*n^30 + (8205205206821582507241410831/467633489356287242458801500939815485440000000000)*n^29 - (1397047442042003310328458927067/719946893349740399647526043029046558720000000000)*n^28 + (493355231131280291188502138255551/4079699062315195598002647577164597166080000000000)*n^27 - (33777214825418933144099085181870319/7217929110249961442620068790368133447680000000000)*n^26 + (48827498451061394784481745605918007/801992123361106826957785421152014827520000000000)*n^25 + (51891701093525335990598359675901071807/8279389273522014595946549494834035425280000000000)*n^24 - (213803054817014232644438466178020893749/370881732937745054363877052469508833280000000000)*n^23 + (15443433038305811114904826221828294914509/556322599406617581545815578704263249920000000000)*n^22 - (79856252165737848868501591300461495585553/92720433234436263590969263117377208320000000000)*n^21 + (18361795140113292412215109940231527559410331/1344446281899325822069054315201969520640000000000)*n^20 + (2176061324274877331030342116674175577957/9099836757494895373545147790786560000000000)*n^19 - (3389469480896218462245599750245235065449649231/133065842335817561530247926127284715520000000000)*n^18 + (88074384897155820686542303857200534962223061533/88710561557211707686831950751523143680000000000)*n^17 - (56147293334838586283262714196447826762349566536039/2262119319708898546014214744163840163840000000000)*n^16 + (15523482981895411063903646904286130760584695099139/39686303854542079754635346388839301120000000000)*n^15 - (16793724149931841456296182121509882526584357321213/9667176579952557888949635658819829760000000000)*n^14 - (15747000443994590528752128569323792336723119688889/146472372423523604378024782709391360000000000)*n^13 + (51090364097878120036795190209636408435200042611964823/13123637368417472749125181266481643520000000000)*n^12 - (1427946277401778612388274773165335540450102986775976101/18591819605258086394594006794182328320000000000)*n^11 + (3117934939120934845413972226936627805891752702356648389/3098636600876347732432334465697054720000000000)*n^10 - (2090861197011171823348862021293384548730891241535729469/258219716739695644369361205474754560000000000)*n^9 + (706957596279365648369572439956083438256540599211447933/57086809926275850789500933171134464000000000)*n^8 + (245102397077635179803442902441528958492923146963600723/351621655343003428775911544894668800000000)*n^7 - (264194369592949367776857058573560316535663034718162816391/23183587808948692737291767860055162880000000)*n^6 + (5552389338260023336297467318149411732360170568100228989/55199018592734982707837542523940864000000)*n^5 - (13428667583902048961741141081989990322041279584124907/23990503167666375704464540401561600000)*n^4 + (33518261207204689673350733318012796035163560559337/18174623611868466442776166970880000)*n^3 - (110155448399543555328855558220247445872856403/46478973627560779243114176000)*n^2 - (665001547436886239033759196317171833/147573547821237938400)*n + 14558439828122760 for n>29
%e Some solutions for n=3
%e ..0..0..1....1..1..1....0..0..0....0..0..0....1..1..1....0..0..1....0..0..1
%e ..0..0..2....1..1..1....0..0..0....0..0..1....1..1..2....0..0..0....1..0..0
%e ..1..0..0....1..1..1....0..0..2....0..0..0....2..0..0....1..0..1....0..0..0
%e ..1..0..1....1..0..0....2..0..0....1..0..2....2..0..0....1..0..0....0..0..2
%K nonn
%O 1,1
%A _R. H. Hardin_ Nov 24 2012
| 