A071042 Number of 0's in n-th row of triangle in A070886.

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, 43, 45, 39, 49, 43, 45, 31, 63, 63, 65, 63, 69, 67, 69, 63, 77, 75, 77, 71, 81, 75, 77, 63, 93, 91, 93, 87, 97, 91, 93, 79, 105, 99, 101, 87, 105, 91, 93, 63, 127, 127, 129, 127

Offset: 0

Author

Hans Havermann, May 26 2002

Keywords

• nonn

Comments

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.

References

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

Links

• Robert Price, Table of n, a(n) for n = 0..999
• A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata...
• S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55 (1983), 601--644.
• Index entries for sequences related to cellular automata

Crossrefs

Cf. A001316, A048967.

Programs

Mathematica

Map[Function[Apply[Plus, Flatten[#1]]],
CellularAutomaton[182, {{1}, 0}, 100]] (* N. J. A. Sloane, Feb 17 2015 *)

PARI

a(n)=2*n-2^hammingweight(n)+1; \\ Altug Alkan, Dec 05 2015

Formula

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

a(2n) = a(n) + 2n, a(2n+1) = 2a(n) + 1. - Ralf Stephan, Oct 07 2003