A071042 - OEIS

%I #27 Oct 15 2018 05:18:52

%S 0,1,3,3,7,7,9,7,15,15,17,15,21,19,21,15,31,31,33,31,37,35,37,31,45,

%T 43,45,39,49,43,45,31,63,63,65,63,69,67,69,63,77,75,77,71,81,75,77,63,

%U 93,91,93,87,97,91,93,79,105,99,101,87,105,91,93,63,127,127,129,127

%N Number of 0's in n-th row of triangle in A070886.

%C Also (omitting initial 0) number of 1's in n-th row of triangle in A071038, that is, number of ON cells at generation n of CA defined by Rule 182.

%D S. Wolfram, A New Kind of Science, Wolfram Media, 2002; Chapter 3.

%H Robert Price, <a href="/A071042/b071042.txt">Table of n, a(n) for n = 0..999</a>

%H A. J. Macfarlane, <a href="http://www.damtp.cam.ac.uk/user/ajm/Papers2016/GFsForCAsOfEvenRuleNo.ps">Generating functions for integer sequences defined by the evolution of cellular automata...</a>

%H S. Wolfram, <a href="http://dx.doi.org/10.1103/RevModPhys.55.601">Statistical mechanics of cellular automata</a>, Rev. Mod. Phys., 55 (1983), 601--644.

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

%F a(n) = 2n + 1 - A001316(n) = n + A048967(n).

%F a(2n) = a(n) + 2n, a(2n+1) = 2a(n) + 1. - _Ralf Stephan_, Oct 07 2003

%t Map[Function[Apply[Plus, Flatten[#1]]],

%t CellularAutomaton[182, {{1}, 0}, 100]] (* _N. J. A. Sloane_, Feb 17 2015 *)

%o (PARI) a(n)=2*n-2^hammingweight(n)+1; \\ _Altug Alkan_, Dec 05 2015

%Y Cf. A001316, A048967.

%K nonn

%O 0,3

%A _Hans Havermann_, May 26 2002