A220005 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal, vertical or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..3 nX3 array

10, 19, 109, 560, 2410, 9094, 32575, 114987, 396917, 1315916, 4156201, 12519404, 36142411, 100533680, 270678655, 708009173, 1804416902, 4491311579, 10939219139, 26113766099, 61178754251, 140820281122, 318767877586

Offset

1,1

Comments

Column 3 of A220010

Links

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

Formula

Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 + (1/152444172305856930250752000000)*n^28 - (1/3350421369359492972544000000)*n^27 + (1/25471039650101408563200000)*n^26 + (43/41363226782215962624000000)*n^25 - (5029/37226904103994366361600000)*n^24 + (870547/91972351315750787481600000)*n^23 - (404867/6797956401598971248640000)*n^22 - (2777213/176570296145427824640000)*n^21 + (157540321/147141913454523187200000)*n^20 - (8521847489/359680232888834457600000)*n^19 - (5896756171/17037484715786895360000)*n^18 + (1999193158206953/46512333274098224332800000)*n^17 - (1754864756699611/1368009802179359539200000)*n^16 + (347465675323531/30066149498447462400000)*n^15 + (5807854993750157/13028664782660567040000)*n^14 - (63962106808513283/3549475982455603200000)*n^13 + (726321071153298251/2662106986841702400000)*n^12 - (148797834273315164401/289685642113592524800000)*n^11 - (611073680485163068111/11587425684543700992000)*n^10 + (1108080234396388175644549/1138050736874827776000000)*n^9 - (58248175543969688527/7702855864704000000)*n^8 + (283282051354077778828369/28513253756123136000000)*n^7 + (1544529331894217156756731/5385836820601036800000)*n^6 - (1108226389277296065072353107/612638938343367936000000)*n^5 - (8742494209572335492077019/2042129794477893120000)*n^4 + (130381592817894359575/1282342100143104)*n^3 - (101179310872363022329/192944991919680)*n^2 + (2861223530470917191/2329089562800)*n - 1126080 for n>10

Example

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

Crossrefs

Sequence in context: A060630 A070199 A015445 * A253213 A293929 A177203

Adjacent sequences: A220002 A220003 A220004 * A220006 A220007 A220008

Keyword

nonn

Author

R. H. Hardin Dec 03 2012

Status

approved