A219709 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array

10, 45, 297, 1860, 9674, 46026, 207161, 881386, 3529403, 13308249, 47441049, 160715914, 520052472, 1614574538, 4827357204, 13942039190, 38993642992, 105830455516, 279212564425, 717166808833, 1795734297356, 4388518752029

Offset

1,1

Comments

Column 3 of A219714

Links

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

Formula

Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 + (1/25407362050976155041792000000)*n^28 + (1/176337966808394366976000000)*n^27 + (31/67215243521100939264000000)*n^26 + (857/33842640094540333056000000)*n^25 + (6701/6204484017332394393600000)*n^24 + (3574927/91972351315750787481600000)*n^23 + (220903/177030114624973209600000)*n^22 + (6281531/176570296145427824640000)*n^21 + (20705161/24523652242420531200000)*n^20 + (58083753499/3237122095999510118400000)*n^19 + (2538631661/7098951964911206400000)*n^18 + (289839269287913/46512333274098224332800000)*n^17 + (22246893795479/228001633696559923200000)*n^16 + (3860442385381/2733286318040678400000)*n^15 + (50577444339493/2714305163054284800000)*n^14 + (3481065292809707/21296855894733619200000)*n^13 + (10517832262098823/3549475982455603200000)*n^12 - (596735921292429571/289685642113592524800000)*n^11 + (34647394351532996977/96561880704530841600000)*n^10 - (117505131104511891379/59897407203938304000000)*n^9 + (509446773110507960443/21075013645830144000000)*n^8 - (5268714537269678496811/28513253756123136000000)*n^7 + (25268032796181630398857/13464592051502592000000)*n^6 - (281231423663326828835501/27847224470153088000000)*n^5 + (10350542927781225635699/340354965746315520000)*n^4 + (4290821665716749/96329785167000)*n^3 - (548747313816628007/964724959598400)*n^2 + (1605025443530933/1164544781400)*n - 1020 for n>5

Example

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

Crossrefs

Sequence in context: A141499 A264553 A278641 * A061772 A032165 A124174

Adjacent sequences: A219706 A219707 A219708 * A219710 A219711 A219712

Keyword

nonn

Author

R. H. Hardin Nov 26 2012

Status

approved