A217457 -id:A217457 - cp's OEIS frontend

A217450 Number of n X 1 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 1 array.

3, 3, 9, 17, 37, 77, 163, 343, 723, 1523, 3209, 6761, 14245, 30013, 63235, 133231, 280707, 591427, 1246089, 2625409, 5531525, 11654477, 24555043, 51735495, 109002515, 229659507, 483874057, 1019483609, 2147969733, 4525598973

Offset: 1

R. H. Hardin, Oct 03 2012

nonn

Column 1 of A217457.

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

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

Empirical: a(n) = 2*a(n-1) + a(n-4).

Empirical g.f.: x*(3 - 3*x + 3*x^2 - x^3) / (1 - 2*x - x^4). - Colin Barker, Feb 19 2018

A217451 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 2 array.

Original entry on oeis.org

3, 15, 69, 253, 1049, 4205, 16887, 68015, 273471, 1100135, 4425449, 17801365, 71607677, 288046417, 1158686263, 4660895899, 18748771139, 75418217399, 303374944277, 1220346484777, 4908927310389, 19746496259789, 79431633434755

Offset: 1

R. H. Hardin, Oct 03 2012

nonn

Column 2 of A217457.

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

R. H. Hardin, Table of n, a(n) for n = 1..128

Cf. A217457.

Empirical: a(n) = 3*a(n-1) + 3*a(n-2) + 6*a(n-3) - 5*a(n-4) + a(n-5) - 17*a(n-6) - 14*a(n-7) - 26*a(n-8) - 4*a(n-9).

Empirical g.f.: x*(3 + 6*x + 15*x^2 - 17*x^3 + 8*x^4 - 43*x^5 - 12*x^6 - 62*x^7 - 12*x^8) / (1 - 3*x - 3*x^2 - 6*x^3 + 5*x^4 - x^5 + 17*x^6 + 14*x^7 + 26*x^8 + 4*x^9). - Colin Barker, Mar 09 2018

A217452 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 3 array.

Original entry on oeis.org

9, 69, 613, 4361, 35067, 271863, 2122623, 16577231, 129398981, 1010161409, 7886865189, 61570433261, 480690831603, 3752745812035, 29297882184787, 228729463311571, 1785699822954649, 13941021624348057, 108838075075791297

Offset: 1

R. H. Hardin, Oct 03 2012

nonn

Column 3 of A217457.

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

R. H. Hardin, Table of n, a(n) for n = 1..43

Cf. A217457.

A217453 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 nX4 array.

Original entry on oeis.org

17, 253, 4361, 60821, 939819, 14031423, 211328743, 3180307843, 47838403809, 719805267377, 10830069725301, 162944007417041, 2451637787845531, 36886610473790015, 554987642859441971, 8350208249838881107

Offset: 1

R. H. Hardin Oct 03 2012

nonn

Column 4 of A217457

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

R. H. Hardin, Table of n, a(n) for n = 1..23

A217454 Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 5 array.

Original entry on oeis.org

37, 1049, 35067, 939819, 28176327, 816124375, 23851967507, 696290061931, 20322202997527, 593290247614087, 17319322866365241, 505587441883441909, 14759372682208435511, 430859457383344897003, 12577815049039384078145

Offset: 1

R. H. Hardin, Oct 03 2012

nonn

Column 5 of A217457.

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

R. H. Hardin, Table of n, a(n) for n = 1..26

Cf. A217457.

A217455 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 nX6 array.

Original entry on oeis.org

77, 4205, 271863, 14031423, 816124375, 45755747495, 2588934295383, 146317423917255, 8268318911401803, 467338335126312183, 26413045308192125181, 1492823071083582045841, 84372932564349811785651

Offset: 1

R. H. Hardin Oct 03 2012

nonn

Column 6 of A217457

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

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

A217449 Number of n X n arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X n array.

Original entry on oeis.org

3, 15, 613, 60821, 28176327, 45755747495, 283827195520911

Offset: 1

R. H. Hardin Oct 03 2012

nonn

Diagonal of A217457

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

A217456 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 nX7 array.

Original entry on oeis.org

163, 16887, 2122623, 211328743, 23851967507, 2588934295383, 283827195520911, 31078249002177539

Offset: 1

R. H. Hardin Oct 03 2012

nonn

Column 7 of A217457

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

cp's OEIS Frontend

A217450 Number of n X 1 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 1 array.

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A217451 Number of n X 2 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 2 array.

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A217452 Number of n X 3 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 3 array.

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A217453 Number of nX4 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 nX4 array.

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A217454 Number of n X 5 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X 5 array.

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A217455 Number of nX6 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 nX6 array.

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A217449 Number of n X n arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 n X n array.

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A217456 Number of nX7 arrays of the minimum value of corresponding elements and their horizontal and vertical neighbors in a random 0..2 nX7 array.

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