A219502 -id:A219502 - cp's OEIS frontend

A219498 Number of n X 4 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..1 n X 4 array.

4, 7, 18, 35, 58, 88, 126, 173, 230, 298, 378, 471, 578, 700, 838, 993, 1166, 1358, 1570, 1803, 2058, 2336, 2638, 2965, 3318, 3698, 4106, 4543, 5010, 5508, 6038, 6601, 7198, 7830, 8498, 9203, 9946, 10728, 11550, 12413, 13318, 14266, 15258, 16295, 17378

Offset: 1

R. H. Hardin, Nov 20 2012

nonn

Column 4 of A219502.

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

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

Cf. A219502.

Empirical: a(n) = (1/6)*n^3 + 1*n^2 + (23/6)*n - 7 for n>2.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(4 - 9*x + 14*x^2 - 11*x^3 + 2*x^4 + x^5) / (1 - x)^4.
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) for n>6.
(End)

A219499 Number of n X 5 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..1 n X 5 array.

Original entry on oeis.org

5, 9, 26, 58, 107, 179, 281, 421, 608, 852, 1164, 1556, 2041, 2633, 3347, 4199, 5206, 6386, 7758, 9342, 11159, 13231, 15581, 18233, 21212, 24544, 28256, 32376, 36933, 41957, 47479, 53531, 60146, 67358, 75202, 83714, 92931, 102891, 113633, 125197

Offset: 1

R. H. Hardin, Nov 20 2012

nonn

Column 5 of A219502.

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

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

Cf. A219502.

Empirical: a(n) = (1/24)*n^4 + (1/4)*n^3 + (35/24)*n^2 + (21/4)*n - 13 for n>2.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(5 - 16*x + 31*x^2 - 32*x^3 + 12*x^4 + 4*x^5 - 3*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)

A219500 Number of n X 6 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..1 n X 6 array.

Original entry on oeis.org

6, 11, 35, 88, 179, 325, 550, 885, 1369, 2050, 2986, 4246, 5911, 8075, 10846, 14347, 18717, 24112, 30706, 38692, 48283, 59713, 73238, 89137, 107713, 129294, 154234, 182914, 215743, 253159, 295630, 343655, 397765, 458524, 526530, 602416, 686851

Offset: 1

R. H. Hardin, Nov 20 2012

nonn

Column 6 of A219502.

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

R. H. Hardin, Table of n, a(n) for n = 1..67

Cf. A219502.

Empirical: a(n) = (1/120)*n^5 + (1/24)*n^4 + (13/24)*n^3 + (59/24)*n^2 + (59/20)*n - 17 for n>3.
Conjectures from Colin Barker, Jul 26 2018: (Start)
G.f.: x*(6 - 25*x + 59*x^2 - 77*x^3 + 46*x^4 - 10*x^6 + x^7 + x^8) / (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>9.
(End)

A219497 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..1 n X n array.

Original entry on oeis.org

2, 3, 11, 35, 107, 325, 995, 3083, 9663, 30581, 97541

Offset: 1

R. H. Hardin Nov 20 2012

nonn

Diagonal of A219502

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

A219501 Number of n X 7 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..1 n X 7 array.

Original entry on oeis.org

7, 13, 45, 126, 281, 550, 995, 1703, 2793, 4424, 6804, 10200, 14949, 21470, 30277, 41993, 57365, 77280, 102782, 135090, 175617, 225990, 288071, 363979, 456113, 567176, 700200, 858572, 1046061, 1266846, 1525545, 1827245, 2177533, 2582528

Offset: 1

R. H. Hardin, Nov 20 2012

nonn

Column 7 of A219502.

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

Cf. A219502.

Empirical: a(n) = (1/720)*n^6 + (1/240)*n^5 + (23/144)*n^4 + (13/16)*n^3 + (331/180)*n^2 + (311/60)*n - 27 for n>3.

cp's OEIS Frontend

A219498 Number of n X 4 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..1 n X 4 array.

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A219499 Number of n X 5 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..1 n X 5 array.

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A219500 Number of n X 6 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..1 n X 6 array.

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A219497 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..1 n X n array.

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Author

Keywords

Comments

Examples

A219501 Number of n X 7 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..1 n X 7 array.

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Author

Keywords

Comments

Examples

Crossrefs

Formula