cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-8 of 8 results.

A221121 Number of n X 3 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

8, 200, 4872, 118472, 2880520, 70036168, 1702839048, 41402332360, 1006644240392, 24475254623432, 595084206353160, 14468703925621448, 351787849605678088, 8553267228797150920, 207961646114893122312, 5056318842606537992392
Offset: 1

Views

Author

R. H. Hardin, Jan 02 2013

Keywords

Comments

Column 3 of A221125.

Examples

			Some solutions for n=3.
..2..1..0....2..1..0....1..1..1....1..1..0....1..0..1....0..1..1....1..2..0
..0..4..0....2..1..0....0..2..0....2..1..0....1..2..0....1..2..0....1..1..0
..1..0..1....2..0..1....3..0..1....3..1..0....2..1..1....1..1..2....1..3..0

Links

Crossrefs

Cf. A221125.

Formula

Empirical: a(n) = 26*a(n-1) - 41*a(n-2).
Conjectures from Colin Barker, Aug 03 2018: (Start)
G.f.: 8*x*(1 - x) / (1 - 26*x + 41*x^2).
a(n) = ((13-8*sqrt(2))^n*(4-7*sqrt(2)) + (4+7*sqrt(2))*(13+8*sqrt(2))^n) / 41.
(End)

A221122 Number of n X 4 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

21, 1950, 179300, 16436223, 1506094707, 138001217828, 12644783009532, 1158616222843158, 106161685080363377, 9727382617196220288, 891300589691816054472, 81668088157651470747218, 7483083373227566657384892
Offset: 1

Views

Author

R. H. Hardin, Jan 02 2013

Keywords

Comments

Column 4 of A221125.

Examples

			Some solutions for n=3:
  1 1 1 0     0 3 1 1     0 2 0 2     1 1 0 1     1 0 2 0
  1 2 1 1     1 1 1 2     1 3 0 1     0 1 3 0     0 3 4 0
  0 1 3 0     0 1 0 1     0 0 1 2     0 3 1 1     0 1 1 0

Links

Crossrefs

Cf. A221125.

Formula

Empirical: a(n) = 109*a(n-1) - 1680*a(n-2) + 8230*a(n-3) - 13300*a(n-4) + 2025*a(n-5) for n>6.
Empirical g.f.: x*(21 - 339*x + 2030*x^2 - 4307*x^3 + 1200*x^4 + 2880*x^5) / (1 - 109*x + 1680*x^2 - 8230*x^3 + 13300*x^4 - 2025*x^5). - Colin Barker, Aug 03 2018

A221126 Number of 2 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

1, 21, 200, 1950, 19005, 185164, 1803949, 17574675, 171218008, 1668058947, 16250746331, 158319795778, 1542400400537, 15026541578483, 146393213915408, 1426207951308175, 13894558811577567, 135365087812821450
Offset: 1

Views

Author

R. H. Hardin, Jan 02 2013

Keywords

Comments

Row 2 of A221125.

Examples

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

Links

Crossrefs

Cf. A221125.

Formula

Empirical: a(n) = 11*a(n-1) - 11*a(n-2) - 12*a(n-3) - 2*a(n-4) for n>6.
Empirical g.f.: x*(1 + 10*x - 20*x^2 - 7*x^3 + 9*x^4 + x^5) / (1 - 11*x + 11*x^2 + 12*x^3 + 2*x^4). - Colin Barker, Aug 04 2018

A221127 Number of 3 X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

1, 144, 4872, 179300, 6405243, 229006550, 8187649472, 292733110656, 10466092166432, 374194374753326, 13378578012147801, 478324533007616827, 17101545371715018992, 611431849960750401963, 21860533596256955469254, 781580038958752812299025, 27943844765222490485325201
Offset: 1

Views

Author

R. H. Hardin, Jan 02 2013

Keywords

Examples

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

Links

Crossrefs

Row 3 of A221125.

A221120 Number of n X n arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

1, 21, 4872, 16436223, 723234356389, 429398881440049645
Offset: 1

Views

Author

R. H. Hardin Jan 02 2013

Keywords

Comments

Diagonal of A221125

Examples

			Some solutions for n=3
..1..0..1....1..1..3....2..0..0....1..1..0....0..3..0....1..0..3....2..0..1
..0..2..1....0..1..0....1..4..0....1..1..3....1..0..2....0..2..1....0..4..0
..3..0..1....1..1..1....0..0..2....1..1..0....0..1..2....0..2..0....0..0..2

A221123 Number of nX5 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

55, 19005, 6405243, 2152770692, 723234356389, 242959402596630, 81617731119238274, 27417937131776836980, 9210537138678339648264, 3094105581109088805200095, 1039406189945536764054814983
Offset: 1

Views

Author

R. H. Hardin Jan 02 2013

Keywords

Comments

Column 5 of A221125

Examples

			Some solutions for n=3
..0..1..1..2..0....0..1..3..0..0....0..1..2..1..0....0..1..3..1..0
..0..3..0..4..1....0..3..0..1..1....0..3..0..1..0....0..4..1..2..1
..0..1..0..1..1....0..3..1..2..0....0..4..2..1..0....0..0..0..1..1

A221124 Number of nX6 arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

144, 185164, 229006550, 282454178707, 348270153038959, 429398881440049645, 529420758866821620887
Offset: 1

Views

Author

R. H. Hardin Jan 02 2013

Keywords

Comments

Column 6 of A221125

Examples

			Some solutions for n=3
..0..1..1..1..4..1....0..1..1..0..2..2....0..1..1..2..1..0....0..1..1..0..3..0
..0..3..1..1..0..1....0..3..1..2..0..2....0..3..3..2..0..0....0..3..3..3..1..0
..0..0..2..0..0..2....0..0..1..1..2..0....0..0..2..0..3..0....0..0..0..1..2..0

A221128 Number of 4Xn arrays of occupancy after each element stays put or moves to some horizontal or antidiagonal neighbor.

Original entry on oeis.org

1, 987, 118472, 16436223, 2152770692, 282454178707, 36946896429843, 4831791752404317, 631836540867287034, 82621661239567004631
Offset: 1

Views

Author

R. H. Hardin Jan 02 2013

Keywords

Comments

Row 4 of A221125

Examples

			Some solutions for n=3
..0..1..0....1..2..1....2..1..0....1..1..0....1..2..1....0..2..1....1..2..0
..2..1..0....1..1..0....0..1..1....2..1..0....0..0..1....0..3..1....1..3..1
..3..1..0....2..0..0....3..2..0....3..1..1....3..1..2....0..1..1....0..0..1
..2..2..0....0..4..0....1..1..0....0..0..2....0..1..0....1..1..1....0..1..2
Showing 1-8 of 8 results.

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