A219686 -id:A219686 - cp's OEIS frontend

A219680 Number of n X 2 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 2 array.

3, 4, 9, 19, 35, 60, 98, 154, 234, 345, 495, 693, 949, 1274, 1680, 2180, 2788, 3519, 4389, 5415, 6615, 8008, 9614, 11454, 13550, 15925, 18603, 21609, 24969, 28710, 32860, 37448, 42504, 48059, 54145, 60795, 68043, 75924, 84474, 93730, 103730, 114513

Offset: 1

R. H. Hardin, Nov 25 2012

nonn

Column 2 of A219686.

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

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

Cf. A219686.

Empirical: a(n) = (1/24)*n^4 - (1/4)*n^3 + (47/24)*n^2 - (7/4)*n for n>2.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(3 - 11*x + 19*x^2 - 16*x^3 + 5*x^4 + 2*x^5 - x^6) / (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>7.
(End)

A219681 Number of nX3 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 nX3 array.

Original entry on oeis.org

6, 8, 31, 99, 269, 655, 1506, 3356, 7278, 15335, 31362, 62286, 120292, 226281, 415250, 744464, 1305597, 2242405, 3775972, 6240154, 10130551, 16171179, 25404010, 39307716, 59953312, 90205963, 133984022, 196588422, 285117878, 408987989

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Column 3 of A219686

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

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

Empirical: a(n) = (1/39916800)*n^11 - (1/3628800)*n^10 + (1/362880)*n^9 + (5/24192)*n^8 - (5639/1209600)*n^7 + (11267/172800)*n^6 - (26249/90720)*n^5 - (45251/36288)*n^4 + (5226461/226800)*n^3 - (303403/3150)*n^2 + (229729/1386)*n - 88 for n>4

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.

Original entry on oeis.org

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

R. H. Hardin, Nov 25 2012

nonn

Column 4 of A219686.

			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

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

Cf. A219686.

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.

A219683 Number of nX5 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 nX5 array.

Original entry on oeis.org

15, 22, 208, 1531, 8964, 44816, 220182, 1116208, 5697556, 28354294, 135630422, 623221049, 2761665622, 11842133497, 49237357701, 198775751684, 780253085746, 2982381614057, 11117260746432, 40470971856226, 144060818799022

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Column 5 of A219686

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

R. H. Hardin, Table of n, a(n) for n = 1..150

A219684 Number of nX6 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 nX6 array.

Original entry on oeis.org

21, 32, 452, 5031, 44736, 344926, 2706117, 22404783, 187497531, 1518906665, 11728070120, 86620862097, 616844079105, 4256996307319, 28523072830335, 185674613829792, 1175484129892778, 7248518396992789, 43607030016608124

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Column 6 of A219686

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

R. H. Hardin, Table of n, a(n) for n = 1..34

A219687 Number of 3 X n 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 3 X n array.

Original entry on oeis.org

6, 9, 31, 87, 208, 452, 922, 1799, 3394, 6234, 11196, 19713, 34085, 57937, 96878, 159429, 258304, 412146, 647840, 1003547, 1532627, 2308645, 3431682, 5036203, 7300766, 10459890, 14818436, 20768893, 28812001, 39581185, 53871318, 72672377

Offset: 1

R. H. Hardin, Nov 25 2012

nonn

Row 3 of A219686.

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

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

Cf. A219686.

Empirical: a(n) = (1/181440)*n^9 - (1/4032)*n^8 + (31/4320)*n^7 - (37/288)*n^6 + (14137/8640)*n^5 - (7859/576)*n^4 + (3420947/45360)*n^3 - (240133/1008)*n^2 + (63709/180)*n - 79 for n>6.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(6 - 51*x + 211*x^2 - 538*x^3 + 913*x^4 - 1055*x^5 + 824*x^6 - 413*x^7 + 110*x^8 + 8*x^9 - 27*x^10 + 23*x^11 - 12*x^12 + x^13 + 3*x^14 - 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>15.
(End)

A219688 Number of 4Xn 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 4Xn array.

Original entry on oeis.org

10, 19, 99, 427, 1531, 5031, 15763, 47784, 140586, 401745, 1116450, 3022129, 7979699, 20573716, 51835099, 127704345, 307858090, 726741861, 1681297548, 3815152314, 8498764539, 18601381870, 40034714647, 84794977698, 176874740063

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Row 4 of A219686

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

R. H. Hardin, Table of n, a(n) for n = 1..125

Empirical: a(n) = (1/71811157608013824000000)*n^25 - (101/17234677825923317760000)*n^24 + (5449/4308669456480829440000)*n^23 - (68021/374666909259202560000)*n^22 + (9824237/510909421717094400000)*n^21 - (21583/13610640605184000)*n^20 + (5371647499/51090942171709440000)*n^19 - (394323599/68948639907840000)*n^18 + (45438295453/175751435059200000)*n^17 - (16515462281/1687213776568320)*n^16 + (542084002355513/1739939207086080000)*n^15 - (28192245777209/3381806039040000)*n^14 + (3250324207416831463/17399392070860800000)*n^13 - (1612171294329183241/463983788556288000)*n^12 + (2781152508058068181/52725430517760000)*n^11 - (757894220102779469/1198305239040000)*n^10 + (37334585059613913334793/6722492391014400000)*n^9 - (107120698751683891/3939922280448)*n^8 - (79214526965365782185939/798295971432960000)*n^7 + (49706772664271871813409/13646084981760000)*n^6 - (2005940155459581015843920483/48784753809792000000)*n^5 + (15777623834516738464154783/54205282010880000)*n^4 - (17331604984082844755616061/12467214862502400)*n^3 + (215362834119633956818141/49473074851200)*n^2 - (4207251609878775049/524924400)*n + 6438609162 for n>14

A219689 Number of 5Xn 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 5Xn array.

Original entry on oeis.org

15, 35, 269, 1688, 8964, 44736, 219216, 1062133, 5046678, 23361295, 105246826, 462379361, 1984693730, 8329188237, 34174571720, 137072090506, 537533392034, 2061741321158, 7738348853856, 28437341923159, 102381325106959

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Row 5 of A219686

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

R. H. Hardin, Table of n, a(n) for n = 1..100

A219690 Number of 6Xn 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 6Xn array.

Original entry on oeis.org

21, 60, 655, 5726, 44816, 344926, 2709320, 21474269, 167685059, 1273322836, 9386203438, 67340577300, 471427290355, 3224592437317, 21562151377146, 141010883018273, 902366368908706, 5653483899077449, 34695071833947322

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Row 6 of A219686

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

R. H. Hardin, Table of n, a(n) for n = 1..41

A219679 Number of n X n 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 n array.

Original entry on oeis.org

3, 4, 31, 427, 8964, 344926, 35011623, 10451333258

Offset: 1

R. H. Hardin Nov 25 2012

nonn

Diagonal of A219686

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

cp's OEIS Frontend

A219680 Number of n X 2 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 2 array.

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A219681 Number of nX3 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 nX3 array.

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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.

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A219683 Number of nX5 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 nX5 array.

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A219684 Number of nX6 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 nX6 array.

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A219687 Number of 3 X n 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 3 X n array.

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A219688 Number of 4Xn 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 4Xn array.

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A219689 Number of 5Xn 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 5Xn array.

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A219690 Number of 6Xn 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 6Xn array.

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A219679 Number of n X n 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 n array.

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