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.

A169789 A169788(2^n).

Original entry on oeis.org

0, 0, 1, 7, 37, 167, 707, 2907, 11787, 47469, 190525
Offset: 0

Views

Author

N. J. A. Sloane, May 13 2010

Keywords

A255748 Total number of ON states after n generations of cellular automaton based on triangles in a 60-degree wedge (see Comments lines for definition).

Original entry on oeis.org

1, 3, 4, 8, 11, 13, 14, 22, 29, 35, 40, 44, 47, 49, 50, 66, 81, 95, 108, 120, 131, 141, 150, 158, 165, 171, 176, 180, 183, 185, 186, 218, 249, 279, 308, 336, 363, 389, 414, 438, 461, 483, 504, 524, 543, 561, 578, 594, 609, 623, 636, 648, 659, 669, 678, 686, 693, 699, 704, 708, 711, 713, 714, 778, 841, 903, 964, 1024
Offset: 1

Views

Author

Omar E. Pol, Mar 30 2015

Keywords

Comments

Also partial sums of A080079.
In order to construct the structure we use the following rules:
On the infinite triangular grid we are in a 60-degree wedge with the vertex located on top of the wedge.
The nearest triangular cell to the vertex remains OFF.
At stage 1, we turn ON the cell whose base is adjacent to the previous OFF cell.
At stage n, in the n-th level of the structure, we turn ON k cells connected by their vertices with their bases up, where k = A080079(n).
The cells turned ON remain ON forever.
The structure seems to grow into the holes of a virtual Sierpiński's triangle (see example).
Note that this is also the structure in every one of the six wedges of the structure of A256266.
A080079 gives the number of cells turned ON at n-th stage.

Examples

			Illustration of initial terms:
-----------------------------------------------------------
n   A080079(n)   a(n)                  Diagram
-----------------------------------------------------------
.                                        / \
1       1         1                     / T \
2       2         3                    / T T \
3       1         4                   /   T   \
4       4         8                  / T T T T \
5       3        11                 /   T T T   \
6       2        13                /     T T     \
7       1        14               /       T       \
8       8        22              / T T T T T T T T \
9       7        29             /   T T T T T T T   \
10      6        35            /     T T T T T T     \
11      5        40           /       T T T T T       \
12      4        44          /         T T T T         \
13      3        47         /           T T T           \
14      2        49        /             T T             \
15      1        50       /               T               \
...
For n = 15 after 15 generations there are 50 ON cells in the structure, so a(15) = 50.

Links

Crossrefs

Cf. A047999, A001316, A080079, A139250, A169779, A169788, A170905, A233970, A256256, A256266.

Programs

  • Mathematica
    Accumulate@ Flatten@ Table[Range[2^n, 1, -1], {n, 0, 6}] (* Michael De Vlieger, Nov 03 2022 *)

Formula

a(n) = A256266(n)/6.
Showing 1-2 of 2 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.