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.

A308973 Langton's ant on a truncated square tiling: number of black cells after n moves of the ant when starting on an octagon and looking towards an edge where the tile meets another octagon.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 8, 7, 8, 9, 10, 11, 10, 11, 10, 9, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 17, 16, 17, 18, 17, 16, 17, 18, 19, 20, 21, 22, 21, 22, 23, 24, 23, 22, 23, 24, 25, 26, 27, 28, 27, 28, 29, 30, 29, 28, 29, 30, 31, 32, 33, 34
Offset: 0

Views

Author

Felix Fröhlich, Jul 04 2019

Keywords

Comments

First differs from A269757 at n = 19.
On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.
On a white octagon, turn 45 degrees right, flip the color of the tile, then move forward one unit.
On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.
On a black octagon, turn 45 degrees left, flip the color of the tile, then move forward one unit.
As in the original variant, order emerges after a transition phase and the ant starts building a recurrent "highway" pattern of 12 steps that repeats indefinitely. - Rémy Sigrist, Jul 21 2019

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A326167, A326352.

Programs

  • PARI
    See Links section.

Formula

a(n + 12) = a(n) + 6 for any n >= 34. - Rémy Sigrist, Jul 21 2019

Extensions

More terms from Rémy Sigrist, Jul 21 2019

A309064 Langton's ant on a snub square tiling: number of black cells after n moves of the ant when starting on a square.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 15, 16, 17, 18, 17, 16, 17, 18, 17, 16, 15, 16, 17, 18, 17, 16, 17, 18, 19, 20, 21, 20, 21, 22
Offset: 0

Views

Author

Felix Fröhlich, Jul 10 2019

Keywords

Comments

First differs from A276073 at n = 16.
On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.
On a white triangle, turn 60 degrees right, flip the color of the tile, then move forward one unit.
On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.
On a black triangle, turn 60 degrees left, flip the color of the tile, then move forward one unit.

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A276073, A308590, A308937, A308973, A326167, A326352.

Formula

a(n+1025) = a(n) + 25 for n > 96420. Lars Blomberg, Aug 15 2019

A309166 Langton's ant on a truncated hexagonal tiling: number of black cells after n moves of the ant when starting on a dodecagon and looking towards an edge where the dodecagon meets a triangle.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 11, 12, 13, 14, 15, 16, 15, 14, 15, 16, 17, 18, 19, 20, 19, 18, 17, 16, 17, 18, 19, 20, 21, 22, 23, 22, 23, 24, 25, 26, 27, 26, 27, 28, 29, 30, 31, 30, 29, 30, 31, 32, 33, 34, 33, 32, 33, 32
Offset: 0

Views

Author

Felix Fröhlich, Jul 15 2019

Keywords

Comments

On a white dodecagon, turn 30 degrees right, flip the color of the tile, then move forward one unit.
On a black dodecagon, turn 30 degrees left, flip the color of the tile, then move forward one unit.
On a white triangle, turn 60 degrees right, flip the color of the tile, then move forward one unit.
On a black triangle, turn 60 degrees left, flip the color of the tile, then move forward one unit.

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064.

Formula

a(n+15) = a(n) + 9 for n > 2034. - Lars Blomberg, Aug 13 2019

Extensions

More terms from Sean A. Irvine, Jul 22 2019

A309241 Langton's ant on a rhombitrihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

Original entry on oeis.org

0, 1, 2, 3, 4, 3, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 11, 12, 13, 14, 15, 16, 15, 14, 13, 12, 11, 10, 11, 10, 9, 8, 7, 8, 9, 10, 11, 12, 13, 12, 13, 14, 13, 12, 13, 14, 15, 16, 15, 14, 15, 14, 13, 14, 15, 14, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 21, 20, 21
Offset: 0

Views

Author

Felix Fröhlich, Jul 17 2019

Keywords

Comments

On a white hexagon, turn 60 degrees right, flip the color of the cell, then move forward one unit.
On a black hexagon, turn 60 degrees left, flip the color of the cell, then move forward one unit.
On a white square, turn 90 degrees right, flip the color of the cell, then move forward one unit.
On a black square, turn 90 degrees left, flip the color of the cell, then move forward one unit.
On a white triangle, turn 60 degrees right, flip the color of the cell, then move forward one unit.
On a black triangle, turn 60 degrees left, flip the color of the cell, then move forward one unit.

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166.

Formula

a(n+448) = a(n). - Lars Blomberg, Aug 16 2019

Extensions

More terms from Lars Blomberg, Aug 16 2019

A309279 Langton's ant on a truncated trihexagonal tiling: number of black cells after n moves of the ant when starting on a dodecagon.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 13, 14, 15, 16, 17, 18, 17, 18, 19, 20, 21, 22, 21, 22, 21, 22, 23, 24, 25, 24, 25, 26, 25, 26, 27, 28, 29, 30, 31, 32, 31, 32, 33, 34, 35, 36, 35, 36, 37, 38, 39, 40, 39, 40, 41, 42, 43, 44, 43, 44, 45, 46, 47, 48, 47, 46
Offset: 0

Views

Author

Felix Fröhlich, Jul 20 2019

Keywords

Comments

On a white dodecagon, turn 30 degrees right, flip the color of the tile, then move forward one unit.
On a black dodecagon, turn 30 degrees left, flip the color of the tile, then move forward one unit.
On a white hexagon, turn 60 degrees right, flip the color of the tile, then move forward one unit.
On a black hexagon, turn 60 degrees left, flip the color of the tile, then move forward one unit.
On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.
On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241.

Extensions

More terms from Sean A. Irvine, Jul 22 2019

A309293 Langton's ant on a snub trihexagonal tiling: number of black cells after n moves of the ant when starting on a hexagon.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 10, 11, 12, 11, 10, 11, 12, 13, 14, 15, 14, 15, 16, 17, 18, 19, 20, 21, 20, 19, 18, 17, 16, 15, 14, 13, 14, 13, 12, 11, 10, 9, 10, 11, 12, 13, 14, 15, 16, 17, 16, 15, 16, 17, 18, 17, 16, 17, 18, 19, 18, 17, 16, 15, 14, 15
Offset: 0

Views

Author

Felix Fröhlich, Jul 21 2019

Keywords

Comments

On a white tile, turn 60 degrees right, flip the color of the tile, then move forward one unit.
On a black tile, turn 60 degrees left, flip the color of the tile, then move forward one unit.
The sequence has a cycle of length of 28292, that is, a(28292)=0 with the ant in the starting hexagon pointing in the start direction, so another cycle will follow. The maximum term in the cycle is a(8148)=174. - Lars Blomberg, Aug 01 2019

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241, A309279.

Extensions

More terms from Lars Blomberg, Aug 01 2019

A309236 Langton's ant on a circular grid with 4-fold rotational symmetry: number of black cells on the grid after n moves of the ant.

Original entry on oeis.org

0, 1, 2, 3, 2, 3, 4, 5, 4, 3, 2, 3, 2, 3, 4, 3, 4, 5, 6, 5, 6, 7, 6, 7, 6, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 6, 7, 6, 5, 4, 3, 4, 5, 6, 5, 6, 5, 6, 7, 6, 7, 6, 7, 6, 5, 4, 5, 6, 7, 6, 7, 8, 9, 8, 7, 6, 7, 6, 7, 6, 7, 8, 7, 8, 7, 8, 9, 10, 9, 8, 7, 6, 7, 6, 5, 4
Offset: 0

Views

Author

Felix Fröhlich, Jul 17 2019

Keywords

Comments

On a white circular segment, turn right to the next edge of the segment, flip the color of that segment, then move onto the segment adjacent to that edge.
On a black circular segment, turn left to the next edge of the segment, flip the color of that segment, then move onto the segment adjacent to that edge.

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A309064, A326167, A326352.

Programs

  • PARI
    lista(nn) = my(c, d=1, x, y, u=1, v=List([])); print1(c); for(n=1, nn, if(x, if(x>#v, listput(v, [1, 1, 1, 1])); if(v[x][y]<0, d=d%4+1, d=(d+2)%4+1); c-=v[x][y]=-v[x][y]; if(d==3, x--; if(!x, d=(y+1)%4+1), x+=d%2; y=(y-d)%4+1), if(u<0, y=(d+2)%4+1, y=d%4+1); c-=u=-u; x=d=1); print1(", ", c)); \\ Jinyuan Wang, Jul 15 2025

Extensions

More terms from Jinyuan Wang, Jul 15 2025

A325631 Langton's ant on an elongated triangular tiling: number of black cells after n moves of the ant when starting on a square and initially looking towards one of the edges where that square meets one of the neighboring triangles.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 4, 5, 6, 7, 8, 9, 8, 9, 10, 11, 12, 13, 12, 13, 14, 15, 14, 13, 14, 15, 16, 15, 16, 17, 16, 15, 16, 17, 18, 17, 16, 15, 16, 17, 18, 19, 20, 19, 18, 19, 20, 19, 20, 21, 22, 23, 24, 23, 22, 23, 22, 23, 22, 21, 20, 19, 18, 19, 18, 17, 18, 19, 20
Offset: 0

Views

Author

Felix Fröhlich, Sep 07 2019

Keywords

Comments

First differs from A276073 at n = 22.
On a white square, turn 90 degrees right, flip the color of the tile, then move forward one unit.
On a white triangle, turn 60 degrees right, flip the color of the tile, then move forward one unit.
On a black square, turn 90 degrees left, flip the color of the tile, then move forward one unit.
On a black triangle, turn 60 degrees left, flip the color of the tile, then move forward one unit.

Examples

			See illustrations in Fröhlich, 2019.

Links

Crossrefs

Cf. A255938, A269757, A308590, A308937, A308973, A326167, A326352, A309064, A309166, A309241, A309279, A309293.

Formula

a(n) = a(n-51) + 11 for n >= 1159. - Jinyuan Wang, Jul 15 2025

Extensions

More terms from Jinyuan Wang, Jul 15 2025
Showing 1-8 of 8 results.

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