A219682 Number of n X 4 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..2 n X 4 array.

10, 14, 87, 427, 1688, 5726, 18486, 59458, 189516, 589078, 1771979, 5155016, 14529474, 39751677, 105748979, 273953703, 692141498, 1707798168, 4120669743, 9734318169, 22538154434, 51195509983, 114191870360, 250314850722

Offset

1,1

Comments

Column 4 of A219686.

Links

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

Formula

Empirical: a(n) = (1/8841761993739701954543616000000)*n^29 - (1/50814724101952310083584000000)*n^28 + (1/580739704022312115240960000)*n^27 - (1/53772194816880751411200000)*n^26 - (67/6768528018908066611200000)*n^25 + (4643/4136322678221596262400000)*n^24 - (1309733/24054307267196359802880000)*n^23 + (776987/2265985467199657082880000)*n^22 + (410911/2972563908172185600000)*n^21 - (490056821/49047304484841062400000)*n^20 + (16372002799/49801878399992463360000)*n^19 - (968981309/631017952436551680000)*n^18 - (17406895711696783/46512333274098224332800000)*n^17 + (8682271622870311/456003267393119846400000)*n^16 - (1074465658101893/2368848142301921280000)*n^15 + (12853594615136699/4342888260886855680000)*n^14 + (3714463850051933851/21296855894733619200000)*n^13 - (16329337796841689161/2366317321637068800000)*n^12 + (563272404080038801903/4456702186362961920000)*n^11 - (41790908888053128958991/38624752281812336640000)*n^10 - (2068970873910075110920537/379350245624942592000000)*n^9 + (12606404340006385030084357/42150027291660288000000)*n^8 - (2180783444974657064143769/497154168055480320000)*n^7 + (96109697881649790417637807/2692918410300518400000)*n^6 - (136580940782604083515955587/928240815671769600000)*n^5 - (1259605322569179919156739/12605739472085760000)*n^4 + (11723883931469901490135337/2431106898187968000)*n^3 - (25408893790340784114283/964724959598400)*n^2 + (5037095951528247967/77636318760)*n - 61265531 for n>13.

Example

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

Crossrefs

Cf. A219686.

Sequence in context: A173684 A258287 A254003 * A167334 A236145 A246769

Adjacent sequences: A219679 A219680 A219681 * A219683 A219684 A219685

Keyword

nonn

Author

R. H. Hardin, Nov 25 2012

Status

approved