A071054 a(2n)=3n+1, a(2n+1)=2n+2.

1, 3, 4, 5, 7, 7, 10, 9, 13, 11, 16, 13, 19, 15, 22, 17, 25, 19, 28, 21, 31, 23, 34, 25, 37, 27, 40, 29, 43, 31, 46, 33, 49, 35, 52, 37, 55, 39, 58, 41, 61, 43, 64, 45, 67, 47, 70, 49, 73, 51, 76, 53, 79, 55, 82, 57, 85, 59, 88, 61, 91, 63, 94, 65, 97, 67, 100, 69

Offset

0,2

Comments

Number of ON cells at n-th generation of 1-D CA defined by Rule 158, starting with a single ON cell at generation 0. Equivalently, number of 1's in n-th row of triangle in A071037. - N. J. A. Sloane, Aug 10 2014

References

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

A. J. Macfarlane, Generating functions for integer sequences defined by the evolution of cellular automata with even rule numbers, 2016.

N. J. A. Sloane, Illustration of first 20 generations of Rule 158

Index entries for sequences related to cellular automata

Formula

G.f.: (-x^3+2x^2+3x+1)/(1-x^2)^2.

a(n) = (5/4)*n + 3/2 + (n/4 - 1/2)*(-1)^n. - Robert Israel, Aug 11 2014

Mathematica

CoefficientList[Series[(-x^3 + 2 x^2 + 3 x + 1)/(1 - x^2)^2, {x, 0, 100}], x] (* Vincenzo Librandi, Aug 11 2014 *)
ArrayPlot[CellularAutomaton[158, {{1}, 0}, 20]] (* N. J. A. Sloane, Aug 11 2014 *)

Crossrefs

Cf. A029578.

Sequence in context: A196122 A247140 A269304 * A379337 A231346 A033545

Adjacent sequences: A071051 A071052 A071053 * A071055 A071056 A071057

Keyword

nonn

Author

Hans Havermann, May 26 2002

Extensions

Simpler definition from N. J. A. Sloane, Aug 11 2014

Status

approved