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 1-4 of 4 results.

A135352 Period 5: repeat [1,2,2,1,3].

Original entry on oeis.org

1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3, 1, 2, 2, 1, 3
Offset: 1

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Author

Roger L. Bagula, Feb 16 2008

Keywords

Comments

This sequence (if extended to be bi-infinite) is the quiddity sequence of the unique width-5 Coxeter frieze pattern A139434; equivalently, if one goes around the (uniquely) triangulated regular pentagon and sequentially looks at its vertices, counting the number of triangles incident with each vertex, then this sequence will be obtained. - Andrey Zabolotskiy, May 04 2023

Links

Crossrefs

Cf. A076839, A139434.

Extensions

Edited by Joerg Arndt, Oct 11 2016
Initial term 1 removed by Joerg Arndt, May 04 2023

A139438 Frieze pattern with 5 rows, read by diagonals.

Original entry on oeis.org

1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1, 1, 1, 2, 3, 1, 1, 3, 5, 2
Offset: 0

Views

Author

N. J. A. Sloane, Jun 09 2008

Keywords

Comments

Period 15: repeat [1, 1, 2, 3, 1, 1, 3, 5, 2, 1, 1, 2, 1, 1, 1]. - Wesley Ivan Hurt, Jun 05 2016

Examples

			The frieze pattern is
... 1 1 1 1 1 1 1 ...
.....1 3 2 1 3 2 ...
....1 2 5 1 2 5 1 ...
.....1 3 2 1 3 2 ...
... 1 1 1 1 1 1 1 ...

Links

Crossrefs

Cf. A139434, A139458.

Formula

Four adjacent entries
...A...
.B...C.
...D...
satisfy D = (BC-1)/A.

A139458 Frieze pattern of order 6, with 5 rows, read by diagonals.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 2, 3, 4, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1, 1, 1, 1, 1, 1, 1, 2, 3, 4
Offset: 0

Views

Author

N. J. A. Sloane, Jun 09 2008

Keywords

Comments

Period 30: repeat [1, 1, 1, 1, 1, 1, 2, 3, 4, 1, 1, 2, 3, 1, 1, 1, 2, 1, 2, 1, 1, 1, 3, 2, 1, 1, 4, 3, 2, 1]. - Wesley Ivan Hurt, Jun 05 2016

Examples

			The frieze pattern is:
... 1 1 1 1 1 1 1 ...
.... 1 2 2 2 1 4 ...
... 3 1 3 3 1 3 8 ...
.... 2 1 4 1 2 2 ...
... 1 1 1 1 1 1 1 ...

Links

Crossrefs

Cf. A139434, A139438.

A111340 Number of positive integer 2-friezes with n-1 nontrivial rows.

Original entry on oeis.org

1, 5, 51, 868, 26952
Offset: 1

Views

Author

N. J. A. Sloane, based on correspondence from James Propp, May 08 2005

Keywords

Comments

The n-th term is the number of positive integer tables a(i,m) (with i running from 1 to n+3 and m running from minus infinity to infinity) subject to the boundary conditions a(i,m) = 0 when i = 1 or i = n+3 and a(i,m) = 1 when i = 2 or i = n+2 and the internal condition a(i,m-1) a(i,m+1) = a(i-1,m) a(i+1,m) + a(i,m) when i is strictly between 2 and n+2.
It is not known as of this writing whether any or all of the terms of the sequence beyond 868 are finite. If the final term "a(i,n)" in the internal condition is replaced by "1", then what we are looking is just a frieze pattern a la Conway and Coxeter (or rather two interlaced frieze patterns that do not interact at all).
According to the lecture notes by S. Morier-Genoud (see paragraph "2-frieze of positive integers"), a(5) is conjectured to be 26952, and it is proved that there are no more finite terms. - Andrei Zabolotskii, Nov 01 2022

Examples

			The number 1 in the sequence is counting the rather boring configuration
    0 0 0 0 0 0 0 0
... 1 1 1 1 1 1 1 1 ...
    1 1 1 1 1 1 1 1
    0 0 0 0 0 0 0 0
The number 5 is counting the configuration
    0 0 0 0 0 0 0 0 0 0
    1 1 1 1 1 1 1 1 1 1
... 1 1 2 3 2 1 1 2 3 2 ...
    1 1 1 1 1 1 1 1 1 1
    0 0 0 0 0 0 0 0 0 0
and its four distinct cyclic shifts, each of which repeats with period 5 (note the Lyness 5-cycle A076839 in the middle).
a(2) = A000108(3) = number of friezes of type A_2 (cyclic shifts of A139434), a(3) = A247415(4). a(4) and a(5) also count friezes of types resp. E_6 and E_8.

Links

Crossrefs

Cf. A000108, A247415, A076839, A139434.

Extensions

The last finite term, a(5), added based on Zhang's preprint and name clarified by Andrei Zabolotskii, May 14 2025
Showing 1-4 of 4 results.

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

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