A256260 Total number of ON states after n generations of a cellular automaton-like on the square grid.

1, 5, 9, 21, 25, 37, 57, 85, 89, 101, 121, 149, 169, 213, 281, 341, 345, 357, 377, 405, 425, 469, 537, 597, 617, 661, 729, 821, 937, 1077, 1241, 1365, 1369, 1381, 1401, 1429, 1449, 1493, 1561, 1621, 1641, 1685, 1753, 1845, 1961, 2101, 2265, 2389, 2409, 2453, 2521, 2613, 2729, 2869, 3033, 3221, 3433, 3669, 3929, 4213, 4521, 4853, 5209, 5461

Offset

1,2

Comments

First differs from A169707 at a(28).

Compare A169707. It appears that both sequences share infinitely many terms, for example: a(1)..a(27), a(31)..a(43), a(47)..a(51), etc.

See also the conjecture in the Example section.

The main entry for this sequence is A256263.

A256261 gives the number of cells turned ON at n-th stage.

Links

Table of n, a(n) for n=1..64.

N. J. A. Sloane, Catalog of Toothpick and Cellular Automata Sequences in the OEIS

Index entries for sequences related to cellular automata

Formula

a(n) = 1 + 4*A256264(n-1).

Example

Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782, the sequence begins:
1;
5;
9,   21;
25,  37, 57, 85;
89, 101,121,149,169,213,281,341;
345,357,377,405,425,469,537,597,617,661,729,821,937,1077,1241,1365;
...
The right border gives the positive terms of A002450.
It appears that this triangle at least shares with the triangles from the following sequences; A147562, A162795, A169707, A255366, A256250, the positive elements of the columns k, if k is a power of 2.

Crossrefs

Cf. A002450, A139250, A147562, A162795, A169707, A255264, A255366, A256250, A256258, A256261, A256263, A256264, A256265.

Sequence in context: A255366 A269522 A169707 * A256250 A256138 A246335

Adjacent sequences: A256257 A256258 A256259 * A256261 A256262 A256263

Keyword

nonn,look

Author

Omar E. Pol, Mar 28 2015

Status

approved