A219377 Number of nX4 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..2 nX4 array

10, 25, 315, 2275, 15256, 88117, 471820, 2391887, 11508779, 52475021, 227321634, 940155612, 3730532377, 14259828254, 52676081028, 188532399603, 655195900069, 2215012029848, 7296267122433, 23450719844938, 73634389866258

Offset

1,1

Comments

Column 4 of A219381

Links

R. H. Hardin, Table of n, a(n) for n = 1..210

Formula

Empirical: a(n) = (1/32327905188896022580370544394201497496149704048640000000000)*n^48 - (1/149666227726370474909122890713895821741433815040000000000)*n^47 + (1/2456527749916111138326029209285828077215023104000000000)*n^46 + (1571/7476388804092512160122697593478607191523983360000000000)*n^45 - (294949/4984259202728341440081798395652404794349322240000000000)*n^44 + (1652977/226557236487651883640081745256927490652241920000000000)*n^43 - (340247/3161263764943979771722070864050151032356864000000000)*n^42 - (632582641/5268772941573299619536784773416918387261440000000000)*n^41 + (5205236441/220297126476932388273315042790951291453440000000000)*n^40 - (68260857631/29655382410356283036792409606474212311040000000000)*n^39 + (328456082167/4349456086852254845396220075616217805619200000000)*n^38 + (39653468878411/2861484267665957135129092155010669608960000000000)*n^37 - (16650599799437419/6032318185890396122704572651103573770240000000000)*n^36 + (266246612902600079/1005386364315066020450762108517262295040000000000)*n^35 - (1215825225928538129/86175974084148516038636752158622482432000000000)*n^34 + (123859420181320931/16129193010402128670333081954822389760000000000)*n^33 + (19784624618853470958401/243730027712743277685033238428427223040000000000)*n^32 - (15368822923061110065089/1692569636894050539479397489086300160000000000)*n^31 + (4945308510840015331857839/8402789261870786387931589470012309504000000000)*n^30 - (831608796604355458877653651/37345730052759050613029286533388042240000000000)*n^29 + (90475390857315106688405357/5203697783565300507656438236179333120000000000)*n^28 + (662779529150507038599794751997/9806968899796143264429441291261050880000000000)*n^27 - (85436532509251512207022043443519/15037352313020753005458476646600278016000000000)*n^26 + (21285123979556945419606949821921637/75186761565103765027292383233001390080000000000)*n^25 - (103856837341129218076114534228567611677/11729134804156187344257611784348216852480000000000)*n^24 + (335143897932265939025784790861629817/3863351384768177649623719296557383680000000000)*n^23 + (2927910312746653834384165830838066927/331144404408700941396318796847775744000000000)*n^22 - (1928426028245916931666220758693496387611/2897513538576133237217789472418037760000000000)*n^21 + (1517444138196238054715512713513237781654121/56018595079138575919543929800082063360000000000)*n^20 - (536204065634052284707393213090726266857321/737086777357086525257156971053711360000000000)*n^19 + (2616970574890777837172806773099955028159143/241292727435615844908182906044142950809600000)*n^18 + (317302631946395328668407914254305384796282213/3696273398217154486951331281313464320000000000)*n^17 - (75616444710428821815605303174511204175309824011/6732497975324102815518496262392381440000000000)*n^16 + (359435597705724778864510250712669749536125805021/906297804370552302089028343014359040000000000)*n^15 - (19988821873148361583172785264125532370449142899/2237772356470499511330934180282368000000000)*n^14 + (307038472104393403555900154635317255946282558781/2288630819117556318406637229834240000000000)*n^13 - (9340583063633628247878798506897191937558716201291079/9295909802629043197297003397091164160000000000)*n^12 - (24351775505405144257298538494560470765787455096836059/2323977450657260799324250849272791040000000000)*n^11 + (3670956144964343347439096594348353306632408580102829/7377706192562732696267463013564416000000000)*n^10 - (596094516928328827527533464377200500281671644869617189/64554929184923911092340301368688640000000000)*n^9 + (1496062337761431061959951437595183571748874815031952927/13478830121481798103076609220962304000000000)*n^8 - (723467545818340040925659593462844760665376223734583127/808729807288907886184596553257738240000000)*n^7 + (7909783917485642362376965609438015813136118214756899751/1931965650745724394774313988337930240000000)*n^6 + (31923179264430782001847735695337077211585515244347661/13799754648183745676959385630985216000000)*n^5 - (387762469069002075607747345732463332113947850442249/1999208597305531308705378366796800000)*n^4 + (53281190030826115148424388000345725263595736223/34951199253593204697646474944000)*n^3 - (410388534374049077112032079714141497580155179/65845212639044437261078416000)*n^2 + (1671700425115600125659587034685043/124011384723729360)*n - 11604668131801676 for n>23

Example

Some solutions for n=3
..0..0..1..1....1..1..2..2....0..0..1..1....0..0..2..2....1..0..1..0
..1..0..1..1....0..0..0..0....1..0..1..1....0..0..2..2....0..0..0..0
..1..1..1..1....0..0..0..0....2..2..1..1....0..0..2..2....0..0..0..0

Crossrefs

Sequence in context: A268303 A248833 A220039 * A156183 A124870 A078257

Adjacent sequences: A219374 A219375 A219376 * A219378 A219379 A219380

Keyword

nonn

Author

R. H. Hardin Nov 19 2012

Status

approved