The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A265722 Number of ON (black) cells in the n-th iteration of the "Rule 1" elementary cellular automaton starting with a single ON (black) cell. 2
 1, 0, 1, 4, 1, 8, 1, 12, 1, 16, 1, 20, 1, 24, 1, 28, 1, 32, 1, 36, 1, 40, 1, 44, 1, 48, 1, 52, 1, 56, 1, 60, 1, 64, 1, 68, 1, 72, 1, 76, 1, 80, 1, 84, 1, 88, 1, 92, 1, 96, 1, 100, 1, 104, 1, 108, 1, 112, 1, 116, 1, 120, 1, 124, 1, 128, 1, 132, 1, 136, 1, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 REFERENCES S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55. LINKS Colin Barker, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Elementary Cellular Automaton FORMULA Conjectures from Colin Barker, Dec 14 2015 and Apr 16 2019: (Start) a(n) = 1/2*(-2*(-1)^n*n+2*n+3*(-1)^n-1). a(n) = 2*a(n-2) - a(n-4) for n>3. G.f.: (1-x^2+4*x^3) / ((1-x)^2*(1+x)^2). (End) a(n) = A019425(n), n>1. - R. J. Mathar, Jan 10 2016 EXAMPLE From Michael De Vlieger, Dec 14 2015: (Start) First 12 rows, replacing zeros with "." for better visibility of ON cells, followed by the total number of 1's per row at right:                       1                        =   1                     . . .                      =   0                   . . 1 . .                    =   1                 1 1 . . . 1 1                  =   4               . . . . 1 . . . .                =   1             1 1 1 1 . . . 1 1 1 1              =   8           . . . . . . 1 . . . . . .            =   1         1 1 1 1 1 1 . . . 1 1 1 1 1 1          =  12       . . . . . . . . 1 . . . . . . . .        =   1     1 1 1 1 1 1 1 1 . . . 1 1 1 1 1 1 1 1      =  16   . . . . . . . . . . 1 . . . . . . . . . .    =   1 1 1 1 1 1 1 1 1 1 1 . . . 1 1 1 1 1 1 1 1 1 1  =  20 (End) MATHEMATICA rule = 1; rows = 30; Table[Total[Table[Take[CellularAutomaton[rule, {{1}, 0}, rows-1, {All, All}][[k]], {rows-k+1, rows+k-1}], {k, 1, rows}][[k]]], {k, 1, rows}] CROSSREFS Cf. A265718, A265720, A265721. Sequence in context: A211779 A318445 A158496 * A019425 A255242 A329371 Adjacent sequences:  A265719 A265720 A265721 * A265723 A265724 A265725 KEYWORD nonn,easy AUTHOR Robert Price, Dec 14 2015 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 6 06:00 EDT 2021. Contains 343580 sequences. (Running on oeis4.)