A220199 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array

10, 36, 238, 1013, 3916, 15067, 58288, 218422, 773169, 2583728, 8224585, 25167752, 74507806, 214204816, 599356409, 1634563737, 4349942989, 11308092511, 28744810615, 71518831786, 174334969663, 416723727408, 977666680868

Offset

1,1

Comments

Column 3 of A220204

Links

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

Formula

Empirical: a(n) = (1/552610124608731372158976000000)*n^29 - (1/38111043076464232562688000000)*n^28 - (43/10888869450418352160768000000)*n^27 + (1013/1209874383379816906752000000)*n^26 - (37/969450627708186624000000)*n^25 + (59/846066002363508326400000)*n^24 + (54830099/390882493091940846796800000)*n^23 - (7939573/894467947578812006400000)*n^22 + (5134253/22071287018178478080000)*n^21 + (37966001/9196369590907699200000)*n^20 - (152257814897/269760174666625843200000)*n^19 + (918505603831/42593711789467238400000)*n^18 - (962278931784007/2907020829631139020800000)*n^17 - (1930456964404139/342002450544839884800000)*n^16 + (43256823284606443/97714985869954252800000)*n^15 - (33779034291676489/2961060177877401600000)*n^14 + (990119936607349039/7098951964911206400000)*n^13 + (8261472616915478693/21296855894733619200000)*n^12 - (14609050016004250375909/289685642113592524800000)*n^11 + (606095725965810479424827/579371284227185049600000)*n^10 - (6894383399300066098456333/569025368437413888000000)*n^9 + (3094992352284156140975351/42150027291660288000000)*n^8 + (7175705615099463540165439/60590664231761664000000)*n^7 - (204006830067393368414683721/26929184103005184000000)*n^6 + (51776746394532001962514261613/612638938343367936000000)*n^5 - (1063830518327474508898879/1954191190887936000)*n^4 + (31834015971911914244845247/14586641389127808000)*n^3 - (480939292908953611199/96472495959840)*n^2 + (10194642893164011521/2329089562800)*n + 2343378 for n>10

Example

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

Crossrefs

Sequence in context: A282554 A240151 A264486 * A089222 A139242 A139236

Adjacent sequences: A220196 A220197 A220198 * A220200 A220201 A220202

Keyword

nonn

Author

R. H. Hardin Dec 07 2012

Status

approved