A220153 -id:A220153 - cp's OEIS frontend

A220154 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.

6, 11, 23, 50, 88, 137, 197, 268, 350, 443, 547, 662, 788, 925, 1073, 1232, 1402, 1583, 1775, 1978, 2192, 2417, 2653, 2900, 3158, 3427, 3707, 3998, 4300, 4613, 4937, 5272, 5618, 5975, 6343, 6722, 7112, 7513, 7925, 8348, 8782, 9227, 9683, 10150, 10628

Offset: 1

R. H. Hardin, Dec 06 2012

nonn

Row 2 of A220153.

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

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

Cf. A220153.

Empirical: a(n) = (11/2)*n^2 - (23/2)*n + 8 for n>2.
Conjectures from Colin Barker, Mar 13 2018: (Start)
G.f.: x*(6 - 7*x + 8*x^2 + 8*x^3 - 4*x^4) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>5.
(End)

A220147 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

Original entry on oeis.org

3, 11, 26, 52, 95, 163, 266, 416, 627, 915, 1298, 1796, 2431, 3227, 4210, 5408, 6851, 8571, 10602, 12980, 15743, 18931, 22586, 26752, 31475, 36803, 42786, 49476, 56927, 65195, 74338, 84416, 95491, 107627, 120890, 135348, 151071, 168131, 186602

Offset: 1

R. H. Hardin, Dec 06 2012

nonn

Column 2 of A220153.

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

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

Cf. A220153.

Empirical: a(n) = (1/12)*n^4 - (1/6)*n^3 + (29/12)*n^2 + (2/3)*n.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(3 - 4*x + x^2 + 2*x^3) / (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>5.
(End)

A220148 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or diagonal 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, 23, 77, 242, 727, 2062, 5493, 13773, 32664, 73654, 158660, 327852, 652215, 1253089, 2331716, 4212805, 7407330, 12701233, 21278447, 34888718, 56073127, 88463032, 137171407, 209299293, 314584340, 466223256, 681905438, 985101192

Offset: 1

R. H. Hardin, Dec 06 2012

nonn

Column 3 of A220153.

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

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

Cf. A220153.

Empirical: a(n) = (1/19958400)*n^11 + (1/725760)*n^10 + (1/145152)*n^9 + (19/120960)*n^8 + (7/3600)*n^7 + (109/34560)*n^6 + (58081/725760)*n^5 + (26759/181440)*n^4 - (400597/907200)*n^3 + (863/126)*n^2 - (2792/495)*n + 5.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(6 - 49*x + 197*x^2 - 484*x^3 + 815*x^4 - 997*x^5 + 934*x^6 - 685*x^7 + 389*x^8 - 161*x^9 + 42*x^10 - 5*x^11) / (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>12.
(End)

A220149 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

Original entry on oeis.org

10, 50, 254, 1174, 5410, 24684, 108169, 448881, 1761976, 6564622, 23314449, 79243936, 258638752, 812875058, 2465906695, 7234818015, 20565976895, 56733702403, 152106586332, 396892051129, 1009207780356, 2503839951948

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 4 of A220153

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

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

Empirical: a(n) = (1/552610124608731372158976000000)*n^29 + (1/7622208615292846512537600000)*n^28 + (1/272221736260458804019200000)*n^27 + (1/1878686930714001408000000)*n^26 + (463/23266815064996478976000000)*n^25 + (127/372269041039943663616000)*n^24 + (97193/2443015581824630292480000)*n^23 + (1458253/2124361375499678515200000)*n^22 + (293509/55178217545446195200000)*n^21 + (1203901/1051013667532308480000)*n^20 + (19197187/20232013099996938240000)*n^19 - (215771663/10648427947366809600000)*n^18 + (47996570583761/2907020829631139020800000)*n^17 - (3130777943459/13680098021793595392000)*n^16 + (352784890291/174491046196346880000)*n^15 + (12242591085947/145409205163622400000)*n^14 - (2308802430337703/1064842794736680960000)*n^13 + (63970460933829533/2129685589473361920000)*n^12 - (7607446827742849/82297057418634240000)*n^11 - (845289139000912665797/289685642113592524800000)*n^10 + (16663286001178049022791/284512684218706944000000)*n^9 - (300232887874952342719/602143247023718400000)*n^8 + (10527514392059792417183/6059066423176166400000)*n^7 + (113898768509462767685501/13464592051502592000000)*n^6 - (19927257308688059839763/149570053306486312500)*n^5 + (32438984170527374840711/44394125966910720000)*n^4 - (955894333256214244573/455832543410244000)*n^3 + (2762815941001472611/964724959598400)*n^2 - (432088153285363/1164544781400)*n - 2315 for n>4

A220150 Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 5 array.

Original entry on oeis.org

15, 88, 645, 4559, 34959, 279304, 2173203, 16032779, 111800304, 739040657, 4649261872, 27940861285, 160944594371, 891059955504, 4752920160872, 24475451373463, 121902117207744, 588193576732660, 2753698006392772

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 5 of A220153.

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

R. H. Hardin, Table of n, a(n) for n = 1..111

Cf. A220153.

A220151 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX6 array.

Original entry on oeis.org

21, 137, 1413, 16110, 214767, 3057777, 42648602, 564936966, 7083618786, 84318189822, 956390845855, 10375891940786, 108038550060777, 1082857046843897, 10473029871107227, 97945268899475975, 887304577889584770

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 6 of A220153

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

R. H. Hardin, Table of n, a(n) for n = 1..27

A220155 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3Xn array.

Original entry on oeis.org

10, 26, 77, 254, 645, 1413, 2841, 5412, 9905, 17565, 30369, 51437, 85641, 140477, 227277, 362851, 571663, 888660, 1362889, 2062054, 3078183, 4534594, 6594369, 9470566, 13438421, 18849815, 26150305, 35899043, 48791933, 65688403, 87642197

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Row 3 of A220153

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

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

Empirical: a(n) = (1/362880)*n^9 + (1/40320)*n^8 - (11/60480)*n^7 - (49/2880)*n^6 + (10837/17280)*n^5 - (30473/5760)*n^4 + (1003267/45360)*n^3 + (41353/3360)*n^2 - (594077/2520)*n + 361 for n>6

A220156 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array.

Original entry on oeis.org

15, 52, 242, 1174, 4559, 16110, 53947, 173732, 539903, 1620236, 4698464, 13180052, 35802185, 94277039, 240952485, 598495844, 1446788180, 3408685943, 7838407335, 17616947657, 38749982170, 83520468048, 176604065342, 366743870453

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Row 4 of A220153

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

R. H. Hardin, Table of n, a(n) for n = 1..121

Empirical: a(n) = (1/969450627708186624000000)*n^25 - (1/4562120600979701760000)*n^24 + (2027/77556050216654929920000)*n^23 - (331/177473799122780160000)*n^22 + (5539/80669908692172800000)*n^21 + (5921/3128016867655680000)*n^20 - (18577907/38318206628782080000)*n^19 + (18754471/474528874659840000)*n^18 - (41570691557/20167477173043200000)*n^17 + (5382522617/73004442255360000)*n^16 - (17042278220257/10439635242516480000)*n^15 + (9851672121271/1491376463216640000)*n^14 + (58162480943607049/52198176212582400000)*n^13 - (135094442095532831/2609908810629120000)*n^12 + (635574550376155319/474528874659840000)*n^11 - (1347751237421517133/59316109332480000)*n^10 + (296554709147396003149/1260467323315200000)*n^9 - (2610520959289132961/4236864952320000)*n^8 - (80984035976231237377421/3193183885731840000)*n^7 + (22349422485612993076363/44349776190720000)*n^6 - (7737663764129137016063569/1524523556556000000)*n^5 + (3378006014145622282711/109727291520000)*n^4 - (83444980373091022514603/820211504112000)*n^3 + (294465474881972180993/4365271310400)*n^2 + (987245448964903837/1487285800)*n - 1630947583 for n>18

A220146 Number of n X n arrays of the minimum value of corresponding elements and their horizontal or diagonal 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, 11, 77, 1174, 34959, 3057777, 822242009, 671848868714

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Diagonal of A220153

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

A220152 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX7 array.

Original entry on oeis.org

28, 197, 2841, 53947, 1272216, 32566283, 822242009, 19788620178, 451988194616, 9825625746882, 204030760833450, 4061291243187050, 77745303520858839, 1435301691794275091

Offset: 1

R. H. Hardin Dec 06 2012

nonn

Column 7 of A220153

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

cp's OEIS Frontend

A220154 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 2 X n array.

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A220147 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 2 array.

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A220148 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 3 array.

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A220149 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX4 array.

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A220150 Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X 5 array.

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A220151 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX6 array.

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A220155 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 3Xn array.

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A220156 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 4Xn array.

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A220146 Number of n X n arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 n X n array.

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A220152 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or diagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and nonincreasing columns, 0..2 nX7 array.

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