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

Author

Hans Havermann, May 26 2002

Keywords

• nonn

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

Crossrefs

Cf. A029578.

Programs

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 *)

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

Extensions

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