A256260 - OEIS

%I #24 Apr 19 2015 22:26:45

%S 1,5,9,21,25,37,57,85,89,101,121,149,169,213,281,341,345,357,377,405,

%T 425,469,537,597,617,661,729,821,937,1077,1241,1365,1369,1381,1401,

%U 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

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

%C First differs from A169707 at a(28).

%C 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.

%C See also the conjecture in the Example section.

%C The main entry for this sequence is A256263.

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

%H N. J. A. Sloane, <a href="/wiki/Catalog_of_Toothpick_and_CA_Sequences_in_OEIS">Catalog of Toothpick and Cellular Automata Sequences in the OEIS</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

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

%e Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782, the sequence begins:

%e 1;

%e 5;

%e 9,   21;

%e 25,  37, 57, 85;

%e 89, 101,121,149,169,213,281,341;

%e 345,357,377,405,425,469,537,597,617,661,729,821,937,1077,1241,1365;

%e ...

%e The right border gives the positive terms of A002450.

%e 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.

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

%K nonn,look

%O 1,2

%A _Omar E. Pol_, Mar 28 2015