A219883 -id:A219883 - cp's OEIS frontend

A219878 Number of nX3 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 nonincreasing columns, 0..2 nX3 array.

6, 11, 47, 146, 410, 1069, 2701, 6645, 15787, 36047, 79071, 166909, 339837, 668982, 1276058, 2363344, 4258060, 7476554, 12815234, 21476998, 35244068, 56710659, 89591851, 139128423, 212611297, 320053673, 475043961, 695818283, 1006597679

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Column 3 of A219883

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

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

Empirical: a(n) = (1/19958400)*n^11 + (1/907200)*n^10 - (1/72576)*n^9 + (29/120960)*n^8 + (31/28800)*n^7 - (263/10800)*n^6 + (175169/362880)*n^5 - (1469677/362880)*n^4 + (901433/56700)*n^3 + (759737/50400)*n^2 - (837073/3960)*n + 342 for n>4

A219879 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 nonincreasing columns, 0..2 nX4 array.

Original entry on oeis.org

10, 17, 129, 621, 2645, 10350, 40239, 155199, 581728, 2085519, 7121374, 23225035, 72683520, 219218974, 639377404, 1808073511, 4967931875, 13286469360, 34640551307, 88162618939, 219292820124, 533661457600, 1271821824645

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Column 4 of A219883

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

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

Empirical: a(n) = (1/1105220249217462744317952000000)*n^29 + (1/38111043076464232562688000000)*n^28 - (1/201645730563302817792000000)*n^27 + (389/604937191689908453376000000)*n^26 - (307/46533630129992957952000000)*n^25 - (773/404640261999938764800000)*n^24 + (40878821/195441246545970423398400000)*n^23 - (70069501/8497445501998714060800000)*n^22 + (12139/477733485241958400000)*n^21 + (50109247/2829652181817753600000)*n^20 - (445566582679/404640261999938764800000)*n^19 + (737417025883/21296855894733619200000)*n^18 - (2216933583028729/5814041659262278041600000)*n^17 - (6268242075250621/342002450544839884800000)*n^16 + (18619463335254179/16285830978325708800000)*n^15 - (536852810288080877/16285830978325708800000)*n^14 + (1152350125136381123/2129685589473361920000)*n^13 - (24885562289413355029/10648427947366809600000)*n^12 - (39408208806540972298007/289685642113592524800000)*n^11 + (1255759711529881816639841/289685642113592524800000)*n^10 - (4460229918485515193847251/63225040937490432000000)*n^9 + (370772167856232917329483/540384965277696000000)*n^8 - (39409170362295331975190999/13464592051502592000000)*n^7 - (280106596148918041437854963/13464592051502592000000)*n^6 + (23189350672718808866722526453/51053244861947328000000)*n^5 - (379821968293133120568499603/102106489723894656000)*n^4 + (3496996713409130344932041/202592241515664000)*n^3 - (3708578246594560887479/83889126921600)*n^2 + (35941859372224430069/776363187600)*n + 10128532 for n>12

A219880 Number of nX5 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 nonincreasing columns, 0..2 nX5 array.

Original entry on oeis.org

15, 24, 292, 2190, 14536, 89795, 565824, 3605746, 22430565, 132945658, 747855900, 4015816403, 20719013269, 103153843621, 496871314897, 2319802248962, 10515430463734, 46349614135168, 198938106785464, 832494580725450

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Column 5 of A219883

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

R. H. Hardin, Table of n, a(n) for n = 1..23

A219884 Number of 3 X n 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 nonincreasing columns, 0..2 3 X n array.

Original entry on oeis.org

10, 21, 47, 129, 292, 600, 1158, 2148, 3863, 6784, 11679, 19763, 32938, 54144, 87860, 140803, 222883, 348483, 538145, 820756, 1236342, 1839593, 2704258, 3928566, 5641847, 8012546, 11257843, 15655113, 21555482, 29399758, 39737040, 53246333

Offset: 1

R. H. Hardin, Nov 30 2012

nonn

Row 3 of A219883.

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

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

Cf. A219883.

Empirical: a(n) = (1/362880)*n^9 - (1/13440)*n^8 + (17/12096)*n^7 - (37/2880)*n^6 + (1813/17280)*n^5 + (1579/5760)*n^4 - (76849/9072)*n^3 + (768487/10080)*n^2 - (590021/2520)*n + 217 for n>6.
Conjectures from Colin Barker, Jul 28 2018: (Start)
G.f.: x*(10 - 79*x + 287*x^2 - 596*x^3 + 697*x^4 - 265*x^5 - 504*x^6 + 984*x^7 - 895*x^8 + 565*x^9 - 351*x^10 + 273*x^11 - 206*x^12 + 112*x^13 - 36*x^14 + 5*x^15) / (1 - x)^10.
a(n) = 10*a(n-1) - 45*a(n-2) + 120*a(n-3) - 210*a(n-4) + 252*a(n-5) - 210*a(n-6) + 120*a(n-7) - 45*a(n-8) + 10*a(n-9) - a(n-10) for n>16.
(End)

A219885 Number of 4Xn 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 nonincreasing columns, 0..2 4Xn array.

Original entry on oeis.org

15, 46, 146, 621, 2190, 6965, 21035, 60891, 171009, 465323, 1225425, 3124293, 7723032, 18545881, 43355303, 98866072, 220320615, 480589189, 1027625310, 2156754843, 4448124037, 9024377209, 18027331364, 35488683485, 68901443927

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Row 4 of A219883

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

R. H. Hardin, Table of n, a(n) for n = 1..78

Empirical: a(n) = (1/15511210043330985984000000)*n^25 - (1/62044840173323943936000)*n^24 + (659/310224200866619719680000)*n^23 - (223/1348800873333129216000)*n^22 + (11969/1751689445887180800000)*n^21 + (13987/175168944588718080000)*n^20 - (307777/9016048618536960000)*n^19 + (218951/80669908692172800)*n^18 - (82167296539/645359269537382400000)*n^17 + (13594532843/3796230997278720000)*n^16 - (148582864867/5965505852866560000)*n^15 - (1842704639807/596550585286656000)*n^14 + (75084344850088337/417585409700659200000)*n^13 - (232073313496988597/41758540970065920000)*n^12 + (200770875484427393/1898115498639360000)*n^11 - (169860589360483739/189811549863936000)*n^10 - (86302000251116357611/5762136335155200000)*n^9 + (405525610427277793513/576213633515520000)*n^8 - (19180292378240586517013/1419192838103040000)*n^7 + (823632212233422499573/5256269770752000)*n^6 - (16853478306444036905959921/16261584603264000000)*n^5 + (8636807269422406550143/6022809112320000)*n^4 + (2309304917571323764033/58203617472000)*n^3 - (428371026518922607544/1159525191825)*n^2 + (1047154147978610871/743642900)*n - 2019003704 for n>23

A219877 Number of n X n 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 nonincreasing columns, 0..2 n X n array.

Original entry on oeis.org

3, 7, 47, 621, 14536, 764027, 113313853

Offset: 1

R. H. Hardin, Nov 30 2012

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

Diagonal of A219883.

A219881 Number of nX6 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 nonincreasing columns, 0..2 nX6 array.

Original entry on oeis.org

21, 32, 600, 6965, 74998, 764027, 8017398, 85092182, 882578607, 8731245391, 82020525701, 735991805511, 6353407612599, 53004720585300, 428371858603213, 3358742175425755

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Column 6 of A219883

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

A219882 Number of nX7 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 nonincreasing columns, 0..2 nX7 array.

Original entry on oeis.org

28, 41, 1158, 21035, 371384, 6337533, 113313853, 2047979807, 36229677541, 611056441694

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Column 7 of A219883

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

A219886 Number of 5Xn 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 nonincreasing columns, 0..2 5Xn array.

Original entry on oeis.org

21, 87, 410, 2645, 14536, 74998, 371384, 1780796, 8327951, 37770000, 165587776, 701557921, 2877746302, 11458190975, 44395384830, 167697083241, 618401792448, 2228478398270, 7854147511367

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Row 5 of A219883

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

A219887 Number of 6Xn 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 nonincreasing columns, 0..2 6Xn array.

Original entry on oeis.org

28, 151, 1069, 10350, 89795, 764027, 6337533, 51044999, 398508546, 2994521086

Offset: 1

R. H. Hardin Nov 30 2012

nonn

Row 6 of A219883

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

cp's OEIS Frontend

A219878 Number of nX3 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 nonincreasing columns, 0..2 nX3 array.

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A219879 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 nonincreasing columns, 0..2 nX4 array.

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A219880 Number of nX5 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 nonincreasing columns, 0..2 nX5 array.

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A219884 Number of 3 X n 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 nonincreasing columns, 0..2 3 X n array.

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A219885 Number of 4Xn 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 nonincreasing columns, 0..2 4Xn array.

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A219877 Number of n X n 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 nonincreasing columns, 0..2 n X n array.

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A219881 Number of nX6 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 nonincreasing columns, 0..2 nX6 array.

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A219882 Number of nX7 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 nonincreasing columns, 0..2 nX7 array.

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A219886 Number of 5Xn 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 nonincreasing columns, 0..2 5Xn array.

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A219887 Number of 6Xn 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 nonincreasing columns, 0..2 6Xn array.

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