A219595 -id:A219595 - cp's OEIS frontend

A219589 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

3, 7, 21, 46, 87, 151, 247, 386, 581, 847, 1201, 1662, 2251, 2991, 3907, 5026, 6377, 7991, 9901, 12142, 14751, 17767, 21231, 25186, 29677, 34751, 40457, 46846, 53971, 61887, 70651, 80322, 90961, 102631, 115397, 129326, 144487, 160951, 178791

Offset: 1

R. H. Hardin, Nov 23 2012

nonn

Column 2 of A219595.

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

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

Cf. A219595.

Empirical: a(n) = (1/12)*n^4 - (1/3)*n^3 + (47/12)*n^2 - (14/3)*n + 2 for n>1.
Conjectures from Colin Barker, Mar 12 2018: (Start)
G.f.: x*(3 - 8*x + 16*x^2 - 19*x^3 + 12*x^4 - 2*x^5) / (1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>6.
(End)

A219590 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 3 array.

Original entry on oeis.org

6, 18, 84, 264, 705, 1739, 4129, 9518, 21271, 46019, 96412, 195879, 386603, 742477, 1389545, 2537385, 4526097, 7895059, 13481452, 22558778, 37028253, 59679103, 94537481, 147328016, 226076963, 341891611, 509957092, 750799089, 1091869239

Offset: 1

R. H. Hardin, Nov 23 2012

nonn

Column 3 of A219595.

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

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

Cf. A219595.

Empirical: a(n) = (1/13305600)*n^11 + (1/1814400)*n^10 - (1/48384)*n^9 + (67/120960)*n^8 - (1009/403200)*n^7 + (403/86400)*n^6 + (106961/241920)*n^5 - (1857341/362880)*n^4 + (10083109/302400)*n^3 - (4379099/50400)*n^2 + (889043/9240)*n - 17 for n>2.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(6 - 54*x + 264*x^2 - 876*x^3 + 2091*x^4 - 3619*x^5 + 4579*x^6 - 4324*x^7 + 3206*x^8 - 1982*x^9 + 1025*x^10 - 397*x^11 + 93*x^12 - 9*x^13) / (1 - x)^12.
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12) for n>14.
(End)

A219591 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

Original entry on oeis.org

10, 34, 233, 1114, 4350, 16117, 60252, 226309, 831045, 2932198, 9899904, 32047091, 99786646, 299774977, 871181292, 2454943142, 6722356023, 17921513868, 46593529264, 118305418513, 293738371262, 713963398966, 1700512384149

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Column 4 of A219595

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

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

Empirical: a(n) = (1/81868166608700944023552000000)*n^29 - (67/33876482734634873389056000000)*n^28 + (1093/7259246300278901440512000000)*n^27 - (1/940621483677214310400000)*n^26 - (47119/62044840173323943936000000)*n^25 + (1869449/24817936069329577574400000)*n^24 - (296052733/86862776242653521510400000)*n^23 + (54522829/1510656978133104721920000)*n^22 + (167845631/29428382690904637440000)*n^21 - (6024199483/14013515567097446400000)*n^20 + (8467657127141/539520349333251686400000)*n^19 - (2932958591041/11358323143857930240000)*n^18 - (12704169291856247/2584018515227679129600000)*n^17 + (47097728297965439/101334059420693299200000)*n^16 - (1011984217642567843/65143323913302835200000)*n^15 + (364057784069101777/1240825217396244480000)*n^14 - (56366476163066975107/28395807859644825600000)*n^13 - (904186645491855977543/14197903929822412800000)*n^12 + (6474020741492280364763/2600993419650662400000)*n^11 - (1166634295507637525043197/25749834854541557760000)*n^10 + (717109824273215889502078381/1517400982499770368000000)*n^9 - (6363461015557560073335283/4014288313491456000000)*n^8 - (11656748989007326967754487087/323150209236062208000000)*n^7 + (3938184473751556080945711017/5385836820601036800000)*n^6 - (163994244837799128753946400473/22690331049754368000000)*n^5 + (30438522365937746680601642677/680709931492631040000)*n^4 - (60274458996187160134975931/347300985455424000)*n^3 + (102759246483272304467447/275635702742400)*n^2 - (195156984499999649389/776363187600)*n - 310620487 for n>13

A219592 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX5 array.

Original entry on oeis.org

15, 55, 550, 4152, 26006, 164075, 1093496, 7362866, 47724022, 292277921, 1695340197, 9384561666, 49848123324, 254860709784, 1257031665966, 5994561288262, 27703365847356, 124331694874481, 542842646444008

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Column 5 of A219595

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

R. H. Hardin, Table of n, a(n) for n = 1..25

A219593 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX6 array.

Original entry on oeis.org

21, 81, 1188, 14793, 156964, 1767430, 21435360, 259297241, 2992271478, 32522357305, 335372829196, 3312669542090, 31487964667940, 288434629481468, 2549339374347045, 21786411636714179, 180452978644995861

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Column 6 of A219595

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

R. H. Hardin, Table of n, a(n) for n = 1..19

A219596 Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

Original entry on oeis.org

6, 21, 84, 233, 550, 1188, 2415, 4684, 8746, 15833, 27945, 48286, 81907, 136629, 224336, 362747, 577797, 906780, 1402432, 2138159, 3214644, 4768098, 6980453, 10091830, 14415652, 20356811, 28433339, 39302076, 53788873, 72923915, 97982798

Offset: 1

R. H. Hardin, Nov 23 2012

nonn

Row 3 of A219595.

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

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

Cf. A219595.

Empirical: a(n) = (1/181440)*n^9 - (1/8064)*n^8 + (11/3780)*n^7 - (107/2880)*n^6 + (749/1728)*n^5 - (1943/1152)*n^4 + (168241/90720)*n^3 + (355057/10080)*n^2 - (306913/2520)*n + 137 for n>3.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(6 - 39*x + 144*x^2 - 382*x^3 + 740*x^4 - 1009*x^5 + 933*x^6 - 554*x^7 + 195*x^8 - 32*x^9 - 5*x^10 + 7*x^11 - 2*x^12) / (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>13.
(End)

A219597 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array.

Original entry on oeis.org

10, 46, 264, 1114, 4152, 14793, 51122, 170728, 550156, 1714425, 5181670, 15217623, 43453991, 120646669, 325663378, 854806408, 2182941966, 5428211529, 13157408701, 31124038143, 71939605189, 162674579688, 360302418944

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Row 4 of A219595

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

R. H. Hardin, Table of n, a(n) for n = 1..143

Empirical: a(n) = (1/32315020923606220800000)*n^25 - (109/11079435745236418560000)*n^24 + (2143/1292600836944248832000)*n^23 - (79003/421500272916602880000)*n^22 + (50173/3193183885731840000)*n^21 - (44960737/43792236147179520000)*n^20 + (27515689/510909421717094400)*n^19 - (60384781/26191528796160000)*n^18 + (21813448039/268899695640576000)*n^17 - (2221068910103/949057749319680000)*n^16 + (9482825036023/173993920708608000)*n^15 - (91557547148539/93211028951040000)*n^14 + (5251971236010727/434984801771520000)*n^13 - (62481716542887379/1491376463216640000)*n^12 - (9282784846386031/3954407288832000)*n^11 + (4293029543793101017/59316109332480000)*n^10 - (105931313393469849253/84031154887680000)*n^9 + (202993929290792591407/13095764398080000)*n^8 - (3712306914099958615759/26609865714432000)*n^7 + (11336104215245400553903/12671364625920000)*n^6 - (369076146776783247776693/101634903770400000)*n^5 + (41196192835097343490679/9034213668480000)*n^4 + (15522433799255326230017/346311523958400)*n^3 - (23040269972514059058427/74209612276800)*n^2 + (112252070661045629/127481640)*n - 1011429662 for n>12

A219598 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 5Xn array.

Original entry on oeis.org

15, 87, 705, 4350, 26006, 156964, 939006, 5466749, 30837420, 168947111, 901097968, 4680202369, 23651533225, 116192356397, 554663937245, 2572846819549, 11600123422679, 50863765123285, 217051630988778, 902189285684499

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Row 5 of A219595

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

R. H. Hardin, Table of n, a(n) for n = 1..37

A219588 Number of n X n arrays of the minimum value of corresponding elements and their horizontal or vertical 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, 84, 1114, 26006, 1767430, 415752625

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Diagonal of A219595

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

A219594 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX7 array.

Original entry on oeis.org

28, 112, 2415, 51122, 939006, 18945258, 415752625, 9020862207, 186931045741, 3664369196641

Offset: 1

R. H. Hardin Nov 23 2012

nonn

Column 7 of A219595

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

cp's OEIS Frontend

A219589 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

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A219590 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 3 array.

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A219591 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

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A219592 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX5 array.

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A219593 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX6 array.

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A219596 Number of 3 X n arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3 X n array.

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A219597 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array.

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A219598 Number of 5Xn arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 5Xn array.

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A219588 Number of n X n arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X n array.

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A219594 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or vertical neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX7 array.

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