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.

A354957 Coordination sequence for the Manhattan hexagonal lattice with respect to the origin.

Original entry on oeis.org

1, 3, 7, 14, 21, 25, 35, 35, 49, 45, 63, 55, 77, 65, 91, 75, 105, 85, 119, 95, 133, 105, 147, 115, 161, 125, 175, 135, 189, 145, 203, 155, 217, 165, 231, 175, 245, 185, 259, 195, 273, 205, 287, 215, 301, 225, 315, 235, 329, 245, 343, 255, 357, 265, 371, 275
Offset: 0

Views

Author

Rémy Sigrist, Jun 13 2022

Keywords

Comments

In the Manhattan hexagonal lattice, streets parallel to one of the 3 axis have alternating orientations:
Z Y
.---<---.
/ \ / \
v ^ ^ v
/ \ / \
.--->---O--->---. X
\ / \ /
v ^ ^ v
\ / \ /
.---<---.

Links

Crossrefs

Cf. A008458, A336627, A354958.

Programs

  • PARI
    See Links section.

A336705 Coordination sequence for the half-Manhattan lattice.

Original entry on oeis.org

1, 3, 7, 12, 16, 20, 24, 28, 32, 36, 40, 44, 48, 52, 56, 60, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 128, 132, 136, 140, 144, 148, 152, 156, 160, 164, 168, 172, 176, 180, 184, 188, 192, 196, 200, 204, 208, 212, 216, 220, 224, 228
Offset: 0

Views

Author

Sean A. Irvine, Jul 31 2020

Keywords

Comments

In the half-Manhattan lattice, E-W streets run alternately E and W, but N-S streets are two way.

Links

Crossrefs

Cf. A336627 (Manhattan lattice), A008574 (square lattice), A336726 (self-avoiding walks), A336742 (self-avoiding cycles).

Programs

  • Mathematica
    LinearRecurrence[{2,-1},{1,3,7,12,16},100] (* Paolo Xausa, Sep 01 2023 *)

Formula

G.f.: (1+x) * (1+2*x^2-x^3) / (1-x)^2.
a(n) = 4*n, n >= 3.

A354958 Coordination sequence for the Manhattan hexagonal lattice with respect to the point (X=0, Y=1).

Original entry on oeis.org

1, 3, 9, 15, 27, 21, 45, 27, 63, 33, 81, 39, 99, 45, 117, 51, 135, 57, 153, 63, 171, 69, 189, 75, 207, 81, 225, 87, 243, 93, 261, 99, 279, 105, 297, 111, 315, 117, 333, 123, 351, 129, 369, 135, 387, 141, 405, 147, 423, 153, 441, 159, 459, 165, 477, 171, 495
Offset: 0

Views

Author

Rémy Sigrist, Jun 13 2022

Keywords

Comments

In the Manhattan hexagonal lattice, streets parallel to one of the 3 axis have alternating orientations:
Z Y
.---<---.
/ \ / \
v ^ ^ v
/ \ / \
.--->---O--->---. X
\ / \ /
v ^ ^ v
\ / \ /
.---<---.

Links

Crossrefs

Cf. A008458, A336627, A354957.

Programs

  • PARI
    See Links section.

A354961 Coordination sequence for the Manhattan cubic lattice.

Original entry on oeis.org

1, 3, 9, 21, 42, 67, 109, 145, 207, 255, 337, 397, 499, 571, 693, 777, 919, 1015, 1177, 1285, 1467, 1587, 1789, 1921, 2143, 2287, 2529, 2685, 2947, 3115, 3397, 3577, 3879, 4071, 4393, 4597, 4939, 5155, 5517, 5745, 6127, 6367, 6769, 7021, 7443, 7707, 8149, 8425
Offset: 0

Views

Author

Rémy Sigrist, Jun 13 2022

Keywords

Comments

In the Manhattan cubic lattice, streets parallel to one of the 3 axis have alternating orientations:
.---->----.
/| /|
v | ^ |
/ v / ^
.----<----. |
| | | |
| .----<|---.
^ / v /
| ^ | v
|/ |/
O---->----.

Links

Crossrefs

Cf. A005899, A336627 A354957.
Showing 1-4 of 4 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.