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.

User: Cody B Duncan

Cody B Duncan's wiki page.

Cody B Duncan has authored 3 sequences.

A335796 Number of ON cells at n-th generation in the "Ulam-Warburton and Friedkin Replicator" hybrid two-dimensional cellular automaton.

Original entry on oeis.org

0, 1, 9, 17, 33, 41, 97, 129, 193, 209, 265, 313, 433, 481, 609, 705, 849, 889, 977, 1073, 1241, 1369, 1641, 1769, 2025, 2089, 2225, 2337, 2601, 2793, 3113, 3337, 3705, 3785, 3921, 4081, 4361, 4601, 5033, 5273, 5641, 5849, 6193, 6449, 6937, 7161, 7641, 7929, 8489, 8625, 8857, 9145
Offset: 0

Views

Author

Cody B Duncan, Jun 24 2020

Keywords

Comments

The 2D CA uses the Moore neighborhood (all eight orthogonally and diagonally adjacent cells are in the neighborhood).
Generation follows the following algorithm: If a cell has an even number of ON neighbors and it is currently OFF, stay OFF; otherwise turn ON.

Crossrefs

Cf. A147562, A247666, A335794

A335795 First differences of A335794.

Original entry on oeis.org

0, 1, 6, 6, 18, 6, 30, 18, 54, 6, 30, 30, 78, 18, 90, 54, 150, 6, 30, 30, 78, 30, 126, 78, 222, 18, 90, 90, 234, 54, 246, 150, 390, 6, 30, 30, 78, 30, 126, 78, 222, 30, 126, 126, 318, 78, 366, 222, 606, 18, 90, 90, 234, 90, 378, 234, 666, 54, 246, 246, 630, 150, 630, 390, 966, 6, 30, 30, 78, 30, 126, 78, 222, 30, 126, 126, 318
Offset: 0

Views

Author

Cody B Duncan, Jun 23 2020

Keywords

Comments

Position of 6 occurs every 2^(n-1) + 1 for n > 0.
Position of 18 appears to occur according to the tetranacci numbers (cf. A000288): 4, 7, 13, 25, 49, ...

Examples

			When written as a triangle:
0
1
6
6 18
6 30 18 54
6 30 30 78 18 90  54 150
6 30 30 78 30 126 78 222 18 90 90 234 54 246 150 390
...

References

  • S. M. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962 (see Example 6, page 224).

Crossrefs

Cf. A000288, A151723, A335794.

A335794 Number of ON cells at n-th generation in an "Ulam-Warburton and Friedkin Replicator" hybrid two-dimensional cellular automaton.

Original entry on oeis.org

0, 1, 7, 13, 31, 37, 67, 85, 139, 145, 175, 205, 283, 301, 391, 445, 595, 601, 631, 661, 739, 769, 895, 973, 1195, 1213, 1303, 1393, 1627, 1681, 1927, 2077, 2467, 2473, 2503, 2533, 2611, 2641, 2767, 2845, 3067, 3097, 3223, 3349, 3667, 3745, 4111, 4333, 4939, 4957
Offset: 0

Views

Author

Cody B Duncan, Jun 23 2020

Keywords

Comments

This 2D CA uses the neighborhood:
[0 X X]
[X X X]
[X X 0]
If a cell has an even number of ON neighbors and it is currently OFF, stay OFF; otherwise turn ON.
The results are similar to those for A151723, but with a distorted grid.
(The "look" keyword refers to the animation. - N. J. A. Sloane, Jul 03 2020)

References

  • S. M. Ulam, On some mathematical problems connected with patterns of growth of figures, pp. 215-224 of R. E. Bellman, ed., Mathematical Problems in the Biological Sciences, Proc. Sympos. Applied Math., Vol. 14, Amer. Math. Soc., 1962 (see Example 6, page 224).

Links

Crossrefs

Cf. A102900, A147562, A151723, A247666, A335795.

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

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