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 1-7 of 7 results.

A183813 1/81 the number of (n+1) X 3 0..2 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

8, 162, 3256, 65640, 1321860, 26630220, 536415300, 10805642100, 217666494900, 4384657426500, 88323978892500, 1779188631250500, 35839769985112500, 721952272492222500, 14542924237284172500, 292951012163242162500
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Comments

Column 2 of A183819.

Examples

			Some solutions with upper left block zero for 5 X 3:
  0 0 0    0 0 0    0 0 1    0 0 2    0 0 1    0 0 0    0 0 2
  0 0 2    0 0 1    0 0 1    0 0 1    0 0 0    0 0 2    0 0 2
  0 1 0    0 2 0    0 1 2    2 1 1    0 2 2    1 1 0    0 2 2
  2 2 1    1 2 0    1 1 2    2 1 2    0 2 2    0 2 1    0 2 1
  1 0 1    1 0 2    1 1 1    0 2 1    0 1 0    1 2 2    2 0 0

Links

Crossrefs

Cf. A183819.

Formula

Empirical: a(n) = 15*a(n-1) + 120*a(n-2) - 330*a(n-3).
Empirical g.f.: 2*x*(4 + 21*x - 67*x^2) / (1 - 15*x - 120*x^2 + 330*x^3). - Colin Barker, Apr 04 2018

A183814 1/81 the number of (n+1) X 4 0..2 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

64, 3256, 163208, 8231592, 414246824, 20864057480, 1050517114472, 52900274426120, 2663752907479720, 134133403972622152, 6754253376412941416, 340109468142471752968, 17126149629153540430376, 862384378029691966195144
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Comments

Column 3 of A183819.

Examples

			Some solutions with upper left block zero for 3 X 4:
..0..0..0..1....0..0..0..1....0..0..0..2....0..0..2..2....0..0..0..2
..0..0..1..1....0..0..1..2....0..0..1..1....0..0..1..0....0..0..2..0
..2..1..1..1....2..0..2..1....2..2..2..1....2..0..0..1....0..2..0..0

Links

Crossrefs

Cf. A183819.

Formula

Empirical: a(n) = 43*a(n-1) + 560*a(n-2) - 10054*a(n-3) + 24480*a(n-4) + 45920*a(n-5).
Empirical g.f.: 8*x*(8 + 63*x - 1580*x^2 + 4218*x^3 + 7624*x^4) / (1 - 43*x - 560*x^2 + 10054*x^3 - 24480*x^4 - 45920*x^5). - Colin Barker, Apr 04 2018

A183812 1/81 the number of (n+1)X(n+1) 0..2 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

1, 162, 163208, 1042063656, 41531687999736, 10425296660739253420
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Diagonal of A183819

Examples

			Some solutions with upper left block zero for 3X3
..0..0..2....0..0..0....0..0..2....0..0..0....0..0..2....0..0..0....0..0..0
..0..0..0....0..0..1....0..0..1....0..0..2....0..0..2....0..0..1....0..0..1
..2..2..0....0..1..2....1..1..1....1..1..1....1..2..1....2..0..1....1..2..1

A183815 1/81 the number of (n+1) X 5 0..2 arrays with no 2 X 2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

512, 65640, 8231592, 1042063656, 131467169720, 16607782066704, 2096961683069192, 264820293988996048, 33441129238755694072, 4223013161022170839808, 533285078101618075961512
Offset: 1

Views

Author

R. H. Hardin, Jan 07 2011

Keywords

Comments

Column 4 of A183819.

Examples

			Some solutions with upper left block zero for 3 X 5
..0..0..2..0..2....0..0..1..1..2....0..0..1..2..0....0..0..2..2..2
..0..0..2..2..1....0..0..2..1..2....0..0..1..2..1....0..0..2..1..1
..0..1..1..2..0....0..2..0..0..1....2..1..1..1..2....0..1..1..0..0

Crossrefs

Cf. A183819.

A183816 1/81 the number of (n+1)X6 0..2 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

4096, 1321860, 414246824, 131467169720, 41531687999736, 13143529051807800, 4156740912572653752
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 5 of A183819

Examples

			Some solutions with upper left block zero for 3X6
..0..0..0..0..1..2....0..0..0..0..1..2....0..0..0..0..0..2....0..0..0..0..2..0
..0..0..1..1..1..2....0..0..1..2..2..0....0..0..1..2..2..0....0..0..2..1..1..0
..0..1..2..2..1..0....1..2..1..0..2..1....2..1..1..1..2..0....1..1..2..0..1..2

A183817 1/81 the number of (n+1)X7 0..2 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

32768, 26630220, 20864057480, 16607782066704, 13143529051807800, 10425296660739253420
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 6 of A183819

Examples

			Some solutions with upper left block zero for 3X7
..0..0..0..0..0..2..1....0..0..0..0..2..0..1....0..0..0..0..2..2..0
..0..0..2..2..1..1..1....0..0..1..1..0..0..1....0..0..2..2..2..2..1
..1..0..1..0..2..1..0....2..0..2..0..1..1..0....1..0..2..0..1..1..0

A183818 1/81 the number of (n+1)X8 0..2 arrays with no 2X2 subblock being a reflection across the shared element pair of any horizontal or vertical neighbor.

Original entry on oeis.org

262144, 536415300, 1050517114472, 2096961683069192, 4156740912572653752
Offset: 1

Views

Author

R. H. Hardin Jan 07 2011

Keywords

Comments

Column 7 of A183819

Examples

			Some solutions with upper left block zero for 3X8
..0..0..0..2..0..2..0..2....0..0..0..1..0..1..0..1....0..0..0..1..0..0..0..2
..0..0..1..1..0..2..1..0....0..0..1..1..0..2..1..0....0..0..1..2..0..2..1..0
..2..1..0..1..0..1..0..1....1..1..0..0..0..0..0..0....1..1..1..2..0..1..0..1
Showing 1-7 of 7 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.