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

0,2

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

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

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*Prod_{k=0..oo} (1+2*x^(2^k)) - Sum_k=0..oo} x^(2^k-1). - N. J. A. Sloane, Aug 09 2014

Example

[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)

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 *)

Crossrefs

Cf. A001316, A000120, A036987, A000225.

Sequence in context: A109823 A337124 A267447 * A212807 A163830 A254931

Adjacent sequences: A071048 A071049 A071050 * A071052 A071053 A071054

Keyword

nonn

Author

Hans Havermann, May 26 2002

Status

approved