A219471 -id:A219471 - cp's OEIS frontend

A219465 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X 2 array.

4, 23, 82, 239, 619, 1471, 3259, 6800, 13464, 25453, 46178, 80755, 136643, 224449, 358927, 560200, 855236, 1279611, 1879594, 2714591, 3859987, 5410427, 7483579, 10224424, 13810120, 18455489, 24419178, 32010547, 41597339, 53614189, 68572031

Offset: 1

R. H. Hardin, Nov 20 2012

nonn

Column 2 of A219471.

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

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

Cf. A219471.

Empirical: a(n) = (1/20160)*n^8 + (1/1260)*n^7 + (1/480)*n^6 + (4/45)*n^5 - (11/960)*n^4 + (277/180)*n^3 + (7607/5040)*n^2 + (61/70)*n.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(4 - 13*x + 19*x^2 - 7*x^3 - 8*x^4 + 10*x^5 - 2*x^6 - x^7) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>9.
(End)

A219466 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX3 array.

Original entry on oeis.org

10, 68, 673, 5040, 32229, 185800, 982456, 4815782, 22059734, 95049799, 387398157, 1500899485, 5551333536, 19675267097, 67041131529, 220243855894, 699365511947, 2151361250171, 6423848162633, 18651881494908, 52745972542258

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Column 3 of A219471

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

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

Empirical: a(n) = (1/523022617466601111760007224100074291200000000)*n^38 + (1/887984070401699680407482553650380800000000)*n^37 + (211/743986653579802434935998896301670400000000)*n^36 + (37/901802004339154466589089571274752000000)*n^35 + (23431/5904655980792082816952372192870400000000)*n^34 + (751/2566497818368045269611288985600000000)*n^33 + (18234521/994634563609361544032084085964800000000)*n^32 + (1202479/1177082323798060998854537379840000000)*n^31 + (3257916313/64169971845765260905295747481600000000)*n^30 + (15998577713/7129996871751695656143971942400000000)*n^29 + (34241128937/386354510291963804027505868800000000)*n^28 + (35548456637/11038700294056108686500167680000000)*n^27 + (10947288367751/101418058951640498557220290560000000)*n^26 + (237907312593869/73758588328465817132523847680000000)*n^25 + (71600877671657743/811344471613123988457762324480000000)*n^24 + (122707098285448223/54089631440874932563850821632000000)*n^23 + (3671970390070217/70641033314117766862602240000000)*n^22 + (1589133646897620433/1483461699596473104114647040000000)*n^21 + (264925397893974283417499/12429925580918848139376627548160000000)*n^20 + (3615125506802045691703/10064717069569917521762451456000000)*n^19 + (99834558409326312420878167/17990681761856227570150381977600000000)*n^18 + (8082599270771039606958097/88189616479687390049756774400000000)*n^17 + (40084616932042931244243721/48294313786495475503438233600000000)*n^16 + (82210406612645728578527/5375990402949403581087744000000)*n^15 + (77521233231877746972047550487/760635442137303739179152179200000000)*n^14 + (318314789653271743306315093267/190158860534325934794788044800000000)*n^13 - (158292888536859409403815888861/17287169139484175890435276800000000)*n^12 + (70868942634763610614565096827/128053104736919821410631680000000)*n^11 - (28239949688137362945250580263751/3978792897182865879544627200000000)*n^10 + (1250965614347251807731812019833/15788860703106610633113600000000)*n^9 - (23380069818927909043317980888257301/43969345581368059511449190400000000)*n^8 + (1533222352111813385357485885877/454604482851199953592320000000)*n^7 - (2368130301559082421877403072112469/97327978500424090064405760000000)*n^6 + (1758899229989365280437101191329/9040100174194737263616000000)*n^5 - (28115613360169956438589192637861/24718216762012467317944320000)*n^4 + (20392529937699678379400434687/4904408087700886372608000)*n^3 - (1495340558417657393233035721/177684955970610344256000)*n^2 + (3623955459298340527/485721041551200)*n - 732 for n>5

A219467 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX4 array.

Original entry on oeis.org

20, 211, 4838, 87083, 1306891, 17399442, 208345624, 2285009931, 23253970439, 221258732227, 1979908560027, 16752069750566, 134676183213583, 1033204910207865, 7592661274649504, 53621665489883610, 364978798507011324

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Column 4 of A219471

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

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

A219468 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX5 array.

Original entry on oeis.org

35, 547, 28159, 1227441, 43792361, 1357658929, 37552353044, 947150536824, 22129769822973, 483036569368799, 9904217535401123, 191717483791553680, 3519902109176030571, 61551065872538233732, 1028861754560712576407

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Column 5 of A219471

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

R. H. Hardin, Table of n, a(n) for n = 1..84

A219469 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX6 array.

Original entry on oeis.org

56, 1248, 143718, 14696377, 1222433026, 86755752059, 5432184254977, 310024709155795, 16405518197790913, 811074258908798713, 37650885062774172715, 1649171050584662652825, 68487713712896868019851

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Column 6 of A219471

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

R. H. Hardin, Table of n, a(n) for n = 1..15

A219472 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 2 X n array.

Original entry on oeis.org

10, 23, 68, 211, 547, 1248, 2663, 5432, 10666, 20206, 36984, 65512, 112528, 187831, 305340, 484415, 751481, 1141999, 1702831, 2495049, 3597241, 5109370, 7157245, 9897666, 13524308, 18274412, 24436354, 32358166, 42457086, 55230217, 71266378

Offset: 1

R. H. Hardin, Nov 20 2012

nonn

Row 2 of A219471.

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

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

Cf. A219471.

Empirical: a(n) = (1/13440)*n^8 + (1/10080)*n^7 + (1/576)*n^6 + (119/720)*n^5 - (9659/5760)*n^4 + (18247/1440)*n^3 - (50047/2016)*n^2 + (6437/840)*n + 13 for n>3.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(10 - 67*x + 221*x^2 - 413*x^3 + 424*x^4 - 153*x^5 - 91*x^6 + 35*x^7 + 124*x^8 - 129*x^9 + 49*x^10 - 7*x^11) / (1 - x)^9.
a(n) = 9*a(n-1) - 36*a(n-2) + 84*a(n-3) - 126*a(n-4) + 126*a(n-5) - 84*a(n-6) + 36*a(n-7) - 9*a(n-8) + a(n-9) for n>12.
(End)

A219473 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 3Xn array.

Original entry on oeis.org

20, 82, 673, 4838, 28159, 143718, 674954, 2941342, 11981143, 45898940, 166443227, 574474013, 1895549798, 6001932167, 18298398284, 53884690148, 153709998598, 425853237243, 1148567805278, 3022012284611, 7771027231688, 19561835095982

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Row 3 of A219471

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

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

Empirical: a(n) = (1/523022617466601111760007224100074291200000000)*n^38 + (1/1448816114865931057506945219113779200000000)*n^37 + (1/21256761530851498141028539894333440000000)*n^36 - (757/247995551193267478311999632100556800000000)*n^35 + (4093/17713967942376248450857116578611200000000)*n^34 + (22907/520999057128713189731091664076800000000)*n^33 - (16139/7957076508874892352256672687718400000)*n^32 + (83764319/994634563609361544032084085964800000000)*n^31 + (549239/75761477976110107326205132800000000)*n^30 - (4678856243/7129996871751695656143971942400000000)*n^29 + (1496226007/25756967352797586935167057920000000)*n^28 - (653413544957/386354510291963804027505868800000000)*n^27 - (2975183387963/50709029475820249278610145280000000)*n^26 + (8806918400800111/811344471613123988457762324480000000)*n^25 - (11812904513950811/23181270617517828241650352128000000)*n^24 + (2067239075526283159/270448157204374662819254108160000000)*n^23 + (5489678448341620139/10384231897175311728802529280000000)*n^22 - (392659222400328327701/10384231897175311728802529280000000)*n^21 + (247423891090169051135981/225998646925797238897756864512000000)*n^20 - (1259752365431022645311581/654206609522044638914559344640000000)*n^19 - (2990270427949071173313147319/2570097394550889652878625996800000000)*n^18 + (1113341390309813951403492457/22047404119921847512439193600000000)*n^17 - (27170930857420612653952304299/28976588271897285302062940160000000)*n^16 - (271137930058645412943527770259/72441470679743213255157350400000000)*n^15 + (535219246244278434476862762431287/760635442137303739179152179200000000)*n^14 - (465297657459368886898913689163269/23769857566790741849348505600000000)*n^13 + (2384764688539478823620118815171/8980347604926844618407936000000)*n^12 - (1530415339594431692136387618041231/1920796571053797321159475200000000)*n^11 - (1852126074867674150037947762929883/51672635028348907526553600000000)*n^10 + (3777985100569138597814021070434363/6140112495652570801766400000000)*n^9 - (18055084608276660939474085529912310323/8793869116273611902289838080000000)*n^8 - (16027148120397118317452245023651668567/229007008236291976622131200000000)*n^7 + (146244839212731141496087089326560146347/111231975429056102930749440000000)*n^6 - (2021853520308780547462644486264447863/173027517334087271225610240000)*n^5 + (1473180274572635724831497308125294809/24718216762012467317944320000)*n^4 - (1282315843815358503748361492528617/8174013479501477287680000)*n^3 + (79251015920672692584467011831459/1243794691794272409792000)*n^2 + (221377469245024941019907/356195430470880)*n - 919752513 for n>16

A219474 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 4Xn array.

Original entry on oeis.org

35, 239, 5040, 87083, 1227441, 14696377, 157191488, 1532762665, 13807624794, 116296337706, 924459750842, 6973773054426, 50113925911679, 344224992704591, 2267656840216326, 14372813464098494, 87897599949502791, 519959958984757538

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Row 4 of A219471

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

R. H. Hardin, Table of n, a(n) for n = 1..92

A219464 Number of n X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X n array.

Original entry on oeis.org

4, 23, 673, 87083, 43792361, 86755752059, 664221777830589

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Diagonal of A219471

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

A219470 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX7 array.

Original entry on oeis.org

84, 2663, 674954, 157191488, 29873644925, 4758315482104, 664221777830589, 85045859176792827

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Column 7 of A219471

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

cp's OEIS Frontend

A219465 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X 2 array.

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A219466 Number of nX3 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX3 array.

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A219467 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX4 array.

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A219468 Number of nX5 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX5 array.

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A219469 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX6 array.

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A219472 Number of 2 X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 2 X n array.

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A219473 Number of 3Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 3Xn array.

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A219474 Number of 4Xn arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 4Xn array.

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A219464 Number of n X n arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 n X n array.

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A219470 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal or antidiagonal neighbors in a random, but sorted with lexicographically nondecreasing rows and columns, 0..3 nX7 array.

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