cp's OEIS Frontend

A070952 Number of 1's in n-th generation of 1-D CA using Rule 30, started with a single 1.

%I A070952 #62 Feb 16 2025 08:32:46
%S A070952 1,3,3,6,4,9,5,12,7,12,11,14,12,19,13,22,15,19,20,24,21,23,23,28,26,
%T A070952 27,26,33,30,34,31,39,26,39,29,46,32,44,38,45,47,41,45,49,38,55,42,51,
%U A070952 44,53,43,59,52,60,49,65,57,60,56,69,61,70,59,78,64,56,65,69,69
%N A070952 Number of 1's in n-th generation of 1-D CA using Rule 30, started with a single 1.
%C A070952 Number of 1's in n-th row of triangle in A070950.
%C A070952 Row sums in A070950; a(n) = 2*n + 1 - A070951(n). - _Reinhard Zumkeller_, Jun 07 2013
%H A070952 N. J. A. Sloane, <a href="/A070952/b070952.txt">Table of n, a(n) for n = 0..10000</a>
%H A070952 N. J. A. Sloane, <a href="/A070952/a070952.png">Illustration of first 20 generations</a>
%H A070952 N. J. A. Sloane, <a href="http://arxiv.org/abs/1503.01168">On the Number of ON Cells in Cellular Automata</a>, arXiv:1503.01168 [math.CO], 2015.
%H A070952 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Rule30.html">Rule 30</a>
%H A070952 Wikipedia, <a href="http://en.wikipedia.org/wiki/Rule_30">Rule 30</a>
%H A070952 <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>
%e A070952 May be arranged into blocks of length 1,1,2,4,8,16,...:
%e A070952 1,
%e A070952 3,
%e A070952 3, 6,
%e A070952 4, 9, 5, 12,
%e A070952 7, 12, 11, 14, 12, 19, 13, 22,
%e A070952 15, 19, 20, 24, 21, 23, 23, 28, 26, 27, 26, 33, 30, 34, 31, 39,
%e A070952 26, 39, 29, 46, 32, 44, 38, 45, 47, 41, 45, 49, 38, 55, 42, 51,
%e A070952     44, 53, 43, 59, 52, 60, 49, 65, 57, 60, 56, 69, 61, 70, 59, 78,
%e A070952 64, 56, 65, 69, 69, ...
%t A070952 Map[Function[Apply[Plus,Flatten[ #1]]], CellularAutomaton[30,{{1},0},100]] (* _N. J. A. Sloane_, Aug 10 2009 *)
%t A070952 SequenceCount[s, {1,0}] + 2 SequenceCount[s, {0,0,1}] (* gives a(n) where s is the sequence for row n-1 *) (* _Trevor Cappallo_, May 01 2021 *)
%o A070952 (Haskell)
%o A070952 a070952 = sum . a070950_row  -- _Reinhard Zumkeller_, Jun 07 2013
%Y A070952 This sequence, A110240, and A245549 all describe the same sequence of successive states. See also A269160.
%Y A070952 Cf. A071049, A070950, A070951, A151929, A051023.
%Y A070952 Cf. A110267 (partial sums), A246023, A246024, A246025, A246026, A246597.
%Y A070952 A265703 is an essentially identical sequence.
%K A070952 nonn,easy,nice
%O A070952 0,2
%A A070952 _N. J. A. Sloane_, May 19 2002, Aug 10 2009
%E A070952 More terms from _Hans Havermann_, May 26 2002
%E A070952 Corrected offset and initial term - _N. J. A. Sloane_, Jun 07 2013