A070952 - OEIS

%I #61 Jan 15 2024 11:01:35

%S 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 27,26,33,30,34,31,39,26,39,29,46,32,44,38,45,47,41,45,49,38,55,42,51,

%U 44,53,43,59,52,60,49,65,57,60,56,69,61,70,59,78,64,56,65,69,69

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

%C Number of 1's in n-th row of triangle in A070950.

%C Row sums in A070950; a(n) = 2*n + 1 - A070951(n). - _Reinhard Zumkeller_, Jun 07 2013

%H N. J. A. Sloane, <a href="/A070952/b070952.txt">Table of n, a(n) for n = 0..10000</a>

%H N. J. A. Sloane, <a href="/A070952/a070952.png">Illustration of first 20 generations</a>

%H 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Rule30.html">Rule 30</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Rule_30">Rule 30</a>

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

%e May be arranged into blocks of length 1,1,2,4,8,16,...:

%e 1,

%e 3,

%e 3, 6,

%e 4, 9, 5, 12,

%e 7, 12, 11, 14, 12, 19, 13, 22,

%e 15, 19, 20, 24, 21, 23, 23, 28, 26, 27, 26, 33, 30, 34, 31, 39,

%e 26, 39, 29, 46, 32, 44, 38, 45, 47, 41, 45, 49, 38, 55, 42, 51,

%e     44, 53, 43, 59, 52, 60, 49, 65, 57, 60, 56, 69, 61, 70, 59, 78,

%e 64, 56, 65, 69, 69, ...

%t Map[Function[Apply[Plus,Flatten[ #1]]], CellularAutomaton[30,{{1},0},100]] (* _N. J. A. Sloane_, Aug 10 2009 *)

%t 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 (Haskell)

%o a070952 = sum . a070950_row  -- _Reinhard Zumkeller_, Jun 07 2013

%Y This sequence, A110240, and A245549 all describe the same sequence of successive states. See also A269160.

%Y Cf. A071049, A070950, A070951, A151929, A051023.

%Y Cf. A110267 (partial sums), A246023, A246024, A246025, A246026, A246597.

%Y A265703 is an essentially identical sequence.

%K nonn,easy,nice

%O 0,2

%A _N. J. A. Sloane_, May 19 2002, Aug 10 2009

%E More terms from _Hans Havermann_, May 26 2002

%E Corrected offset and initial term - _N. J. A. Sloane_, Jun 07 2013