cp's OEIS Frontend

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

%I A256260 #24 Apr 19 2015 22:26:45
%S A256260 1,5,9,21,25,37,57,85,89,101,121,149,169,213,281,341,345,357,377,405,
%T A256260 425,469,537,597,617,661,729,821,937,1077,1241,1365,1369,1381,1401,
%U A256260 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 A256260 Total number of ON states after n generations of a cellular automaton-like on the square grid.
%C A256260 First differs from A169707 at a(28).
%C A256260 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 A256260 See also the conjecture in the Example section.
%C A256260 The main entry for this sequence is A256263.
%C A256260 A256261 gives the number of cells turned ON at n-th stage.
%H A256260 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 A256260 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%F A256260 a(n) = 1 + 4*A256264(n-1).
%e A256260 Written as an irregular triangle T(j,k), k>=1, in which the row lengths are the terms of A011782, the sequence begins:
%e A256260 1;
%e A256260 5;
%e A256260 9,   21;
%e A256260 25,  37, 57, 85;
%e A256260 89, 101,121,149,169,213,281,341;
%e A256260 345,357,377,405,425,469,537,597,617,661,729,821,937,1077,1241,1365;
%e A256260 ...
%e A256260 The right border gives the positive terms of A002450.
%e A256260 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 A256260 Cf. A002450, A139250, A147562, A162795, A169707, A255264, A255366, A256250, A256258, A256261, A256263, A256264, A256265.
%K A256260 nonn,look
%O A256260 1,2
%A A256260 _Omar E. Pol_, Mar 28 2015