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 1-6 of 6 results.

A161357 Longer side (x) of inner rectangle described in A168339.

Original entry on oeis.org

1, 3, 3, 4, 3, 4, 5, 5, 6, 5, 7, 6, 5, 7, 6, 8, 7, 7, 8, 8, 7, 9, 9, 8, 7, 9, 9, 8, 10, 10, 9, 9, 11, 10, 10, 9, 11, 11, 11, 10, 9, 12, 11, 11, 10, 13, 12, 12, 11, 11, 13, 13, 15, 12, 11, 14, 13, 13, 13, 12, 11, 14, 14, 13, 13, 12, 15, 15, 14, 14, 13, 13, 15, 15, 15, 14, 14, 13, 16, 16
Offset: 1

Views

Author

R. H. Hardin and N. J. A. Sloane, Nov 27 2009

Keywords

Crossrefs

Cf. A161358, A168339. Equals A143082 + 2.

Formula

a(n) = A143082(n)-2. [From R. J. Mathar, Mar 06 2010]

Extensions

Extended with output of the variable dimn of the progr. in A168339 - R. J. Mathar, Mar 06 2010

A161358 Shorter side (x) of inner rectangle described in A168339.

Original entry on oeis.org

1, 1, 2, 2, 3, 3, 3, 3, 3, 4, 3, 4, 5, 4, 5, 4, 5, 5, 5, 5, 6, 5, 5, 6, 7, 6, 6, 7, 6, 6, 7, 7, 6, 7, 7, 8, 7, 7, 7, 8, 9, 7, 8, 8, 9, 7, 8, 8, 9, 9, 8, 8, 7, 9, 10, 8, 9, 9, 9, 10, 11, 9, 9, 10, 10, 11, 9, 9, 10, 10, 11, 11, 10, 10, 10, 11, 11, 12, 10, 10, 9, 11, 11, 12, 13, 9, 11, 11, 12, 12, 13, 11, 11, 11, 12, 12
Offset: 1

Views

Author

R. H. Hardin and N. J. A. Sloane, Nov 27 2009

Keywords

Crossrefs

Cf. A161357, A168339. Equals A145288(n)-2.

Extensions

Corrected definition and flipped sign in the formula - R. J. Mathar, Mar 06 2010

A143082 Longer side (k) of bordered rectangle described in A168339.

Original entry on oeis.org

3, 5, 5, 6, 5, 6, 7, 7, 8, 7, 9, 8, 7, 9, 8, 10, 9, 9, 10, 10, 9, 11, 11, 10, 9, 11, 11, 10, 12, 12, 11, 11, 13, 12, 12, 11, 13, 13, 13, 12, 11, 14, 13, 13, 12, 15, 14, 14, 13, 13, 15, 15, 17, 14, 13, 16, 15, 15, 15, 14, 13, 16, 16, 15, 15, 14, 17, 17, 16, 16, 15, 15, 17, 17, 17, 16
Offset: 1

Views

Author

R. H. Hardin and N. J. A. Sloane, Nov 27 2009

Keywords

Crossrefs

Cf. A145299, A168339. Equals A161357 - 2.

Formula

a(n) = A161357(n)+2. [From R. J. Mathar, Mar 06 2010]

Extensions

Extended with output of the program in A168339, variable dimn+2, by R. J. Mathar, Mar 06 2010

A145288 Shorter side (l) of bordered rectangle described in A168339.

Original entry on oeis.org

3, 3, 4, 4, 5, 5, 5, 5, 5, 6, 5, 6, 7, 6, 7, 6, 7, 7, 7, 7, 8, 7, 7, 8, 9, 8, 8, 9, 8, 8, 9, 9, 8, 9, 9, 10, 9, 9, 9, 10, 11, 9, 10, 10, 11, 9, 10, 10, 11, 11, 10, 10, 9, 11, 12, 10, 11, 11, 11, 12, 13, 11, 11, 12, 12, 13, 11, 11, 12, 12, 13, 13, 12, 12, 12, 13, 13, 14, 12, 12, 11, 13, 13
Offset: 1

Views

Author

R. H. Hardin and N. J. A. Sloane, Nov 27 2009

Keywords

Crossrefs

Cf. A143082, A168339.

Formula

a(n) = A161358(n) + 2.

Extensions

Added more terms (output dimm+2 of the program in A168339) - R. J. Mathar, Mar 05 2010
Formula corrected by Michel Marcus, Feb 16 2014

A161359 Number of squares in inner rectangle described in A168339.

Original entry on oeis.org

0, 1, 3, 4, 4, 6, 8, 7, 9, 10, 10, 12, 12, 14, 15, 16, 18, 17, 21, 20, 21, 23, 22, 24, 24, 28, 27, 28, 31, 30, 32, 31, 33, 36, 35, 36, 40, 39, 38, 40, 40, 42, 45, 44, 45, 45, 49, 48, 50, 49, 53, 52, 52, 54, 55, 56, 60, 59, 58, 60, 60, 64, 63, 66, 65, 66, 68, 67, 71, 70, 72, 71
Offset: 1

Views

Author

R. H. Hardin and N. J. A. Sloane, Nov 27 2009

Keywords

Crossrefs

Cf. A168339, A161369.

Formula

a(n) = A168339(n) - 2*(A161357(n)+A161358(n)) - 4.

Extensions

More terms (variables cost-2*(dimm+dimn)-4 of the C program in A168339) added by R. J. Mathar, Mar 06 2010

A118797 Number of cells in smallest polyomino with n holes.

Original entry on oeis.org

7, 11, 14, 17, 19, 23, 25, 28, 30, 33, 35, 38, 40, 43, 45, 48, 50, 53, 55, 57, 59, 62, 64, 67, 69, 71, 74, 76, 78, 81, 83, 85, 88, 90, 92, 95, 97, 99, 101, 104, 106, 108, 110, 113, 115, 117, 119, 122, 124, 126, 128, 131, 133, 135, 137, 140, 142, 144, 146, 149
Offset: 1

Views

Author

Franklin T. Adams-Watters, May 22 2006

Keywords

Comments

The polyomino must be rook-wise connected and a hole is a collection of rook-wise connected empty cells from which a rook cannot escape. - N. J. A. Sloane, May 25 2006
From Dmitry Kamenetsky, Feb 28 2017: (Start)
There is a simple pattern that gives us a good upper bound. The idea is to use two rows of single-cell holes touching at their corners:
XXXXXXXXXXX
X X X X X X
XX X X X X X
XXXXXXXXXXX
Each new hole requires an additional 3 cells (X) to surround it. Hence we get a(n) <= 3n + 5. (End)

Examples

			a(1) = 7 from
  XX
  X X
  XXX

Links

Crossrefs

Cf. A168339.

Extensions

a(8) added by Dmitry Kamenetsky, Feb 28 2017
a(9)-a(60) added by Peter Kagey, Oct 28 2019, from Table 2 of the Malen Roldán paper.
Showing 1-6 of 6 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.