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 1-2 of 2 results.

A226595 Lengths of maximal nontouching increasing paths in n X n grids.

Original entry on oeis.org

0, 2, 4, 7, 9, 12, 15, 17, 20, 24, 27, 29, 33, 36, 39
Offset: 1

Views

Author

Charles R Greathouse IV and Giovanni Resta, Jun 13 2013

Keywords

Comments

The path is not allowed to touch itself, not even on single points. "Increasing" means that the (Euclidean) length of each line segment must be strictly longer than the last.

Examples

			An example for a(8)=17
-------------------------
01 02  .  .  .  . 05  .
..  . 03  . 04  .  . 18
09 07  .  . 06  .  . 16
..  .  .  .  .  .  . 14
..  .  .  .  .  .  . 12
..  . 08  .  .  .  .  .
10 17 15 13  .  .  .  .
..  .  .  . 11  .  .  .
-------------------------

Links

Crossrefs

Cf. A226596.

Formula

a(n) <= A226596(n) <= A160663(n-1).

Extensions

a(10)-a(12) from Joseph DeVincentis via Charles R Greathouse IV, Oct 08 2015
a(13) from Charles R Greathouse IV, Oct 25 2015 using code from Joseph DeVincentis
a(14)-a(15) from Bert Dobbelaere, Oct 05 2018

A358212 a(n) is the maximal possible sum of squares of the side lengths of an n^2-gon supported on a subset 1 <= x,y <= n of an integer lattice.

Original entry on oeis.org

4, 10, 36, 98, 232
Offset: 2

Views

Author

Giedrius Alkauskas, Nov 04 2022

Keywords

Comments

Examples show that a(7) >= 462, a(8) >= 842, a(9) >= 1424, a(10) >= 2242.
Asymptotics: liminf a(n)/n^4 >= 8/27, limsup a(n)/n^4 <= 2/3.

Links

Crossrefs

Cf. A209077, A110611, A064842, A226595, A226596.

Extensions

a(5) from Giedrius Alkauskas, Oct 09 2023
a(6) from Giedrius Alkauskas, Nov 30 2023
Showing 1-2 of 2 results.

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

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