A070952 Number of 1's in n-th generation of 1-D CA using Rule 30, started with a single 1.

1, 3, 3, 6, 4, 9, 5, 12, 7, 12, 11, 14, 12, 19, 13, 22, 15, 19, 20, 24, 21, 23, 23, 28, 26, 27, 26, 33, 30, 34, 31, 39, 26, 39, 29, 46, 32, 44, 38, 45, 47, 41, 45, 49, 38, 55, 42, 51, 44, 53, 43, 59, 52, 60, 49, 65, 57, 60, 56, 69, 61, 70, 59, 78, 64, 56, 65, 69, 69

Offset

0,2

Comments

Number of 1's in n-th row of triangle in A070950.

Row sums in A070950; a(n) = 2*n + 1 - A070951(n). - Reinhard Zumkeller, Jun 07 2013

Links

N. J. A. Sloane, Table of n, a(n) for n = 0..10000

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

N. J. A. Sloane, On the Number of ON Cells in Cellular Automata, arXiv:1503.01168 [math.CO], 2015.

Eric Weisstein's World of Mathematics, Rule 30

Wikipedia, Rule 30

Index entries for sequences related to cellular automata

Example

May be arranged into blocks of length 1,1,2,4,8,16,...:
1,
3,
3, 6,
4, 9, 5, 12,
7, 12, 11, 14, 12, 19, 13, 22,
15, 19, 20, 24, 21, 23, 23, 28, 26, 27, 26, 33, 30, 34, 31, 39,
26, 39, 29, 46, 32, 44, 38, 45, 47, 41, 45, 49, 38, 55, 42, 51,
    44, 53, 43, 59, 52, 60, 49, 65, 57, 60, 56, 69, 61, 70, 59, 78,
64, 56, 65, 69, 69, ...

Mathematica

Map[Function[Apply[Plus, Flatten[ #1]]], CellularAutomaton[30, {{1}, 0}, 100]] (* N. J. A. Sloane, Aug 10 2009 *)
SequenceCount[s, {1, 0}] + 2 SequenceCount[s, {0, 0, 1}] (* gives a(n) where s is the sequence for row n-1 *) (* Trevor Cappallo, May 01 2021 *)

Prog

(Haskell)
a070952 = sum . a070950_row  -- Reinhard Zumkeller, Jun 07 2013

Crossrefs

This sequence, A110240, and A245549 all describe the same sequence of successive states. See also A269160.

Cf. A071049, A070950, A070951, A151929, A051023.

Cf. A110267 (partial sums), A246023, A246024, A246025, A246026, A246597.

A265703 is an essentially identical sequence.

Sequence in context: A349392 A069734 A265703 * A137462 A163926 A362334

Adjacent sequences: A070949 A070950 A070951 * A070953 A070954 A070955

Keyword

nonn,easy,nice

Author

N. J. A. Sloane, May 19 2002, Aug 10 2009

Extensions

More terms from Hans Havermann, May 26 2002

Corrected offset and initial term - N. J. A. Sloane, Jun 07 2013

Status

approved