A071051 Number of 1's in n-th row of triangle in A071035.

1, 3, 4, 7, 4, 8, 8, 15, 4, 8, 8, 16, 8, 16, 16, 31, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 63, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 64, 8, 16, 16, 32, 16, 32, 32, 64, 16, 32, 32, 64, 32, 64, 64, 127, 4, 8, 8, 16, 8, 16, 16, 32, 8, 16

Offset: 0

Author

Hans Havermann, May 26 2002

Keywords

• nonn

Comments

Number of ON cells at generation n of 1-D CA defined by Rule 126, starting with a single ON cell. - N. J. A. Sloane, Aug 09 2014

Examples

			[Contribution from _Omar E. Pol_, Dec 11 2010] (Start)
May be arranged in blocks of sizes 1, 1, 2, 4, 8, 16, 32, ...:
1,
3,
4, 7,
4, 8, 8, 15,
4, 8, 8, 16, 8, 16, 16, 31,
4, 8, 8, 16, 8, 16, 16, 32, 8, 16, 16, 32, 16, 32, 32, 63,
Last terms of rows give positive terms of A000225.
(End)
		

References

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

Links

• Robert Price, Table of n, a(n) for n = 0..1000
• A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata...
• N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.
• 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, A000120, A036987, A000225.

Programs

Mathematica

a[n_] := 2^(DigitCount[n, 2, 1]+1) - Boole[IntegerQ[Log[2, n+1]]];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Oct 02 2018, from 2nd formula *)

Formula

a(2n) = a(n)+A036987(n); a(2n+1) = a(n)+2*2^A000120(n). - Benoit Cloitre, Sep 22 2003

a(n) = 2^(1+wt(n)) unless n is of the form 2^i-1 in which case we must subtract 1, where wt = A000120. - N. J. A. Sloane, Aug 09 2014

G.f.: 2*Product_{k>=0} (1+2*x^(2^k)) - Sum_{k>=0} x^(2^k-1). - N. J. A. Sloane, Aug 09 2014