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

Author

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

Keywords

• nonn
• easy
• nice

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

Examples

			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, ...
		

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

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.

Programs

Haskell

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

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 *)

Extensions

More terms from Hans Havermann, May 26 2002

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