A220032 -id:A220032 - cp's OEIS frontend

A220029 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..1 n X 5 array.

5, 12, 30, 61, 111, 187, 297, 450, 656, 926, 1272, 1707, 2245, 2901, 3691, 4632, 5742, 7040, 8546, 10281, 12267, 14527, 17085, 19966, 23196, 26802, 30812, 35255, 40161, 45561, 51487, 57972, 65050, 72756, 81126, 90197, 100007, 110595, 122001, 134266

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Column 5 of A220032.

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

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

Cf. A220032.

Empirical: a(n) = (1/24)*n^4 + (5/12)*n^3 + (11/24)*n^2 + (61/12)*n - 4 for n>1.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(5 - 13*x + 20*x^2 - 19*x^3 + 11*x^4 - 3*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)

A220030 Number of n X 6 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..1 n X 6 array.

Original entry on oeis.org

6, 15, 42, 95, 192, 358, 626, 1038, 1646, 2513, 3714, 5337, 7484, 10272, 13834, 18320, 23898, 30755, 39098, 49155, 61176, 75434, 92226, 111874, 134726, 161157, 191570, 226397, 266100, 311172, 362138, 419556, 484018, 556151, 636618, 726119, 825392

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Column 6 of A220032.

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

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

Cf. A220032.

Empirical: a(n) = (1/120)*n^5 + (1/8)*n^4 + (5/24)*n^3 + (15/8)*n^2 + (227/60)*n - 4 for n>1.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(3 - 6*x + 6*x^2 - 2*x^3)*(2 - 3*x + 4*x^2 - 2*x^3) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>7.
(End)

A220031 Number of n X 7 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..1 n X 7 array.

Original entry on oeis.org

7, 18, 55, 137, 302, 613, 1165, 2094, 3587, 5893, 9335, 14323, 21368, 31097, 44269, 61792, 84741, 114377, 152167, 199805, 259234, 332669, 422621, 531922, 663751, 821661, 1009607, 1231975, 1493612, 1799857, 2156573, 2570180, 3047689, 3596737

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Column 7 of A220032.

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

R. H. Hardin, Table of n, a(n) for n = 1..68

Cf. A220032.

Empirical: a(n) = (1/720)*n^6 + (7/240)*n^5 + (11/144)*n^4 + (25/48)*n^3 + (263/90)*n^2 + (29/20)*n - 4 for n>2.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(7 - 31*x + 76*x^2 - 115*x^3 + 113*x^4 - 66*x^5 + 17*x^6 + x^7 - x^8) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>9.
(End)

A220033 Number of 3 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..1 3 X n array.

Original entry on oeis.org

4, 6, 10, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, 867, 910, 954, 999, 1045, 1092, 1140, 1189, 1239, 1290, 1342, 1395, 1449, 1504, 1560, 1617, 1675

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Row 3 of A220032.

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

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

Cf. A220032.

Empirical: a(n) = (1/2)*n^2 + (13/2)*n - 15 for n>3.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(4 - 6*x + 4*x^2 + 3*x^3 - 3*x^4 - x^5) / (1 - x)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n>6.
(End)

A220034 Number of 4 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..1 4 X n array.

Original entry on oeis.org

5, 8, 15, 34, 61, 95, 137, 187, 246, 315, 395, 487, 592, 711, 845, 995, 1162, 1347, 1551, 1775, 2020, 2287, 2577, 2891, 3230, 3595, 3987, 4407, 4856, 5335, 5845, 6387, 6962, 7571, 8215, 8895, 9612, 10367, 11161, 11995, 12870, 13787, 14747, 15751, 16800

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Row 4 of A220032.

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

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

Cf. A220032.

Empirical: a(n) = (1/6)*n^3 + (1/2)*n^2 + (43/3)*n - 45 for n>5.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(5 - 12*x + 13*x^2 + 2*x^3 - 12*x^4 + 3*x^5 + 2*x^6 - x^7 + x^8) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>9.
(End)

A220035 Number of 5 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..1 5 X n array.

Original entry on oeis.org

6, 10, 21, 55, 111, 192, 302, 442, 618, 838, 1111, 1447, 1857, 2353, 2948, 3656, 4492, 5472, 6613, 7933, 9451, 11187, 13162, 15398, 17918, 20746, 23907, 27427, 31333, 35653, 40416, 45652, 51392, 57668, 64513, 71961, 80047, 88807, 98278, 108498

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Row 5 of A220032.

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

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

Cf. A220032.

Empirical: a(n) = (1/24)*n^4 - (1/12)*n^3 + (95/24)*n^2 + (289/12)*n - 132 for n>6.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(6 - 20*x + 31*x^2 - 10*x^3 - 24*x^4 + 21*x^5 - 3*x^6 - 4*x^7 + 8*x^8 - 3*x^9 - x^10) / (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>11.
(End)

A220036 Number of 6 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..1 6 X n array.

Original entry on oeis.org

7, 12, 28, 83, 187, 358, 613, 962, 1426, 2034, 2823, 3839, 5137, 6782, 8850, 11429, 14620, 18538, 23313, 29091, 36035, 44326, 54164, 65769, 79382, 95266, 113707, 135015, 159525, 187598, 219622, 256013, 297216, 343706, 395989, 454603, 520119

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Row 6 of A220032.

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

R. H. Hardin, Table of n, a(n) for n = 1..155

Cf. A220032.

Empirical: a(n) = (1/120)*n^5 - (1/12)*n^4 + (47/24)*n^3 - (23/12)*n^2 + (1771/30)*n - 323 for n>8.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(7 - 30*x + 61*x^2 - 45*x^3 - 26*x^4 + 59*x^5 - 35*x^6 + 3*x^7 + 24*x^8 - 21*x^9 + 3*x^10 + x^11 - x^12 + x^13) / (1 - x)^6.
a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n>14.
(End)

A220037 Number of 7 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..1 7 X n array.

Original entry on oeis.org

8, 14, 36, 119, 297, 626, 1165, 1963, 3088, 4630, 6711, 9492, 13175, 18010, 24304, 32431, 42843, 56082, 72793, 93738, 119811, 152054, 191674, 240061, 298807, 369726, 454875, 556576, 677439, 820386, 988676, 1185931, 1416163, 1683802, 1993725

Offset: 1

R. H. Hardin, Dec 03 2012

nonn

Row 7 of A220032.

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

R. H. Hardin, Table of n, a(n) for n = 1..53

Cf. A220032.

Empirical: a(n) = (1/720)*n^6 - (7/240)*n^5 + (107/144)*n^4 - (209/48)*n^3 + (1609/45)*n^2 + (1913/60)*n - 813 for n>9.
Conjectures from Colin Barker, Jul 30 2018: (Start)
G.f.: x*(8 - 42*x + 106*x^2 - 119*x^3 + 10*x^4 + 108*x^5 - 123*x^6 + 58*x^7 + 36*x^8 - 68*x^9 + 33*x^10 - 10*x^11 - 2*x^12 + 10*x^13 - 3*x^14 - x^15) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>16.
(End)

A220028 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..1 n X n array.

Original entry on oeis.org

2, 4, 10, 34, 111, 358, 1165, 3789, 12375, 40583, 133632, 441773

Offset: 1

R. H. Hardin Dec 03 2012

nonn

Diagonal of A220032

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

cp's OEIS Frontend

A220029 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..1 n X 5 array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220030 Number of n X 6 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..1 n X 6 array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220031 Number of n X 7 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..1 n X 7 array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220033 Number of 3 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..1 3 X n array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220034 Number of 4 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..1 4 X n array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220035 Number of 5 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..1 5 X n array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220036 Number of 6 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..1 6 X n array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220037 Number of 7 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..1 7 X n array.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Formula

A220028 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..1 n X n array.

Views

Author

Keywords

Comments

Examples