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A070952
Number of 1's in n-th generation of 1-D CA using Rule 30, started with a single 1.
24
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, 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
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. A110267 (partial sums), A246023, A246024, A246025, A246026, A246597.
A265703 is an essentially identical sequence.
Sequence in context: A349392 A069734 A265703 * A137462 A163926 A362334
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