A245549 -id:A245549 - cp's OEIS frontend

A110240 Decimal form of binary integer produced by the ON cells at n-th generation following Wolfram's Rule 30 cellular automaton starting from a single ON-cell represented as 1.

1, 7, 25, 111, 401, 1783, 6409, 28479, 102849, 456263, 1641433, 7287855, 26332369, 116815671, 420186569, 1865727615, 6741246849, 29904391303, 107568396185, 477630335215, 1725755276049, 7655529137527, 27537575631497

Offset: 0

Alexandre Wajnberg and Eric Angelini, Sep 06 2005

See A245549 for binary equivalents. See A070952 for number of ON cells. - N. J. A. Sloane, Jul 28 2014
For n > 0: 3 < a(n+1) / a(n) < 5, floor(a(n+1)/a(n)) = A010702(n+1). - Reinhard Zumkeller, Jun 08 2013
Iterates of A269160 starting from a(0) = 1. See also A269168. - Antti Karttunen, Feb 20 2016
Also, the decimal representation of the n-th generation of the "Rule 66847740" 5-neighbors elementary cellular automaton starting with a single ON (black) cell. - Philipp O. Tsvetkov, Jul 17 2019

			a(1)=1 because the automaton begins at first "generation" with one black cell: 1;
a(2)=5 because one black cell, through Rule 30 at 2nd generation, produces three contiguous black cells: 111 (binary), so 7 (decimal);
a(3)=25 because the third generation is "black black white white black" cells: 11001, so 25 (decimal).

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000
Erica Jen, Global properties of cellular automata, Journal of Statistical Physics 43 (1986), pp. 219-242.
Antti Karttunen, Terms up to a(255) drawn as binary strings, with 1 bit = 3x3 pixels resolution
Antti Karttunen, Terms up to a(1023) drawn as binary strings, with 1 bit = 1 pixel resolution
N. J. A. Sloane, Illustration of first 20 generations
Eric Weisstein's World of Mathematics, Rule 30.
Stephen Wolfram, Announcing the Rule 30 Prizes, 2019
Index entries for sequences related to cellular automata

Cf. A030101, A070950, A051023, A092539, A092540, A070952 (number of ON cells, the binary weight of terms), A100053, A100054, A100055, A094603, A094604, A000225, A074890, A010702, A245549, A269160, A269162.
Cf. A269165 (indices of ones in this sequence).
Cf. A269166 (a left inverse).
Left edge of A269168.
Cf. also A265281, A328106.
For bitwise XOR (and OR) combinations with other such 1D CA trajectories, see for example: A327971, A327972, A327973, A327976, A328103, A328104.

a110240 = foldl (\v d -> 2 * v + d) 0 . map toInteger . a070950_row
-- Reinhard Zumkeller, Jun 08 2013

rows = 23; ca = CellularAutomaton[30, {{1}, 0}, rows-1]; Table[ FromDigits[ ca[[k, rows-k+1 ;; rows+k-1]], 2], {k, 1, rows}] (* Jean-François Alcover, Jun 07 2012 *)

A269160(n) = bitxor(n, bitor(2*n, 4*n));
A110240(n) = if(!n,1,A269160(A110240(n-1))); \\ Antti Karttunen, Oct 05 2019

def A269160(n): return(n^((n<<1)|(n<<2)))
def genA110240():
    '''Yield successive terms of A110240 (Rule 30) starting from A110240(0)=1.'''
    s = 1
    while True:
       yield s
       s = A269160(s)
def take(n, g):
    '''Returns a list composed of the next n elements returned by generator g.'''
    z = []
    if 0 == n: return(z)
    for x in g:
        z.append(x)
        if n > 1: n = n-1
        else: return(z)
take(30, genA110240())
# Antti Karttunen, Oct 05 2019

;; With memoization-macro definec.
(definec (A110240 n) (if (zero? n) 1 (A269160 (A110240 (- n 1)))))
;; Antti Karttunen, Feb 20 2016

From Antti Karttunen, Feb 20 2016: (Start)
a(0) = 1, for n >= 1, a(n) = A269160(a(n-1)).
a(n) = A030101(A265281(n)). [The rule 30 is the mirror image of the rule 86.]
A269166(a(n)) = n for all n >= 0. (End)
From Antti Karttunen, Oct 05 2019: (Start)
For n >= 1, a(n) = a(n-1) XOR 2*A328104(n-1).
For n >= 1, a(n) = 2*a(n-1) XOR A327973(n). (End)

More terms from Eric W. Weisstein, Apr 08 2006

Offset corrected by Reinhard Zumkeller, Jun 08 2013

A070950 Triangle read by rows giving successive states of cellular automaton generated by "Rule 30".

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1

Offset: 0

N. J. A. Sloane, May 19 2002

If cell and right-hand neighbor are both 0 then new state of cell = state of left-hand neighbor; otherwise new state is complement of that of left-hand neighbor.
A simple rule which produces apparently random behavior. "... probably the single most surprising discovery I have ever made" - Stephen Wolfram.
Row n has length 2n+1.
A110240(n) = A245549(n) = value of row n, seen as binary number. - Reinhard Zumkeller, Jun 08 2013
A070952 gives number of ON cells. - N. J. A. Sloane, Jul 28 2014

			Triangle begins:
        1;
      1,1,1;
    1,1,0,0,1;
  1,1,0,1,1,1,1;
  ...

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 27.

Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
N. J. A. Sloane, Illustration of initial terms
Eric Weisstein's World of Mathematics, Rule 30
S. Wolfram, A New Kind of Science
Index to Elementary Cellular Automata
Index entries for sequences related to cellular automata

Cf. A070951, A070952 (row sums), A051023 (central terms).
Cf. A071032 (mirror image, rule 86), A226463 (complemented, rule 135), A226464 (mirrored and complemented, rule 149).
Cf. A363343 (diagonals from the right), A363344 (diagonals from the left).
Cf. A094605 (periods of diagonals from the right), A363345 (eventual periods of diagonals from the left), A363346 (length of initial transients on diagonals from the left).
Cf. also A245549, A110240.

a070950 n k = a070950_tabf !! n !! k
a070950_row n = a070950_tabf !! n
a070950_tabf = iterate rule30 [1] where
   rule30 row = f ([0,0] ++ row ++ [0,0]) where
       f [,]          = []
       f (u:ws@(0:0:_)) = u : f ws
       f (u:ws)         = (1 - u) : f ws
-- Reinhard Zumkeller, Feb 01 2013

ArrayPlot[CellularAutomaton[30,{{1},0}, 50]] (* N. J. A. Sloane, Aug 11 2009 *)
Clear[t, n, k]; nn = 10; t[1, k_] := t[1, k] = If[k == 3, 1, 0];
t[n_, k_] := t[n, k] = Mod[t[-1 + n, -2 + k] + t[-1 + n, -1 + k] + (1 + t[-1 + n, -1 + k]) t[-1 + n, k], 2]; Flatten[Table[Table[t[n, k], {k, 3, 2*n + 1}], {n, 1, nn}]] (*Mats Granvik,Dec 08 2019*)

From Mats Granvik, Dec 06 2019: (Start)
The following recurrence expresses the rules in rule 30, except that instead of If, Or, And, Not, we use addition, subtraction, and multiplication.
T(n, 1) = 0
T(n, 2) = 0
T(1, 3) = 1
T(n, k) = [2*n + 1 >= k] ((1 - (T(n - 1, k - 2)*T(n - 1, k - 1)*T(n - 1, k)))*(1 - T(n - 1, k - 2)*T(n - 1, k - 1)*(1 - T(n - 1, k)))*(1 - (T(n - 1, k - 2)*(1 - T(n - 1, k - 1))*T(n - 1, k)))*(1 - ((1 - T(n - 1, k - 2))*(1 - T(n - 1, k - 1))*(1 - T(n - 1, k))))) + ((T(n - 1, k - 2)*(1 - T(n - 1, k - 1))*(1 - T(n - 1, k)))*((1 - T(n - 1, k - 2))*T(n - 1, k - 1)*T(n - 1, k))*((1 - T(n - 1, k - 2))*T(n - 1, k - 1)*(1 - T(n - 1, k)))*((1 - T(n - 1, k - 2))*(1 - T(n - 1, k - 1))*T(n - 1, k))).
Discarding the term after the plus sign, multiplying/expanding the terms out and replacing all exponents with ones, gives us this simplified recurrence:
T(n, 1) = 0
T(n, 2) = 0
T(1, 3) = 1
T(n, k) = T(-1 + n, -2 + k) + T(-1 + n, -1 + k) - 2 T(-1 + n, -2 + k) T(-1 + n, -1 + k) + (-1 + 2 T(-1 + n, -2 + k)) (-1 + T(-1 + n, -1 + k)) T(-1 + n, k).
That in turn simplifies to:
T(n, 1) = 0
T(n, 2) = 0
T(1, 3) = 1
T(n, k) = Mod(T(-1 + n, -2 + k) + T(-1 + n, -1 + k) + (1 + T(-1 + n, -1 + k)) T(-1 + n, k), 2).
(End)

More terms from Hans Havermann, May 24 2002

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

Original entry on oeis.org

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

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

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

			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, ...

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

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.

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

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 *)

More terms from Hans Havermann, May 26 2002

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

A265122 Binary representation of the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 0, 10101, 0, 101111101, 10001000, 1010001000101, 1000100000, 10111000100011101, 1010100010101000, 101000000010000000101, 111110001111100000, 1011101000101010001011101, 101000100000001000101000, 10100000100011111000100000101, 11100010100010100011100000

Offset: 0

Robert Price, Dec 01 2015

			From _Michael De Vlieger_, Dec 02 2015: (Start)
First 8 rows, showing surrounding context at left, cells generated by the initial cell at center, and the binary equivalent at right where leading zeros are lost:
0                   1                 ->                 1
1                 0 0 0               ->                 0
0               1 0 1 0 1             ->             10101
1             0 0 0 0 0 0 0           ->                 0
0           1 0 1 1 1 1 1 0 1         ->         101111101
1         0 0 0 1 0 0 0 1 0 0 0       ->          10001000
0       1 0 1 0 0 0 1 0 0 0 1 0 1     ->     1010001000101
1     0 0 0 0 0 1 0 0 0 1 0 0 0 0 0   ->        1000100000
0   1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1 -> 10111000100011101
(End)

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
S. Wolfram, A New Kind of Science
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A245549.

rule = 73; rows = 20; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]]], {k,1,rows}]

A327980 Distances between successive zeros in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

Original entry on oeis.org

4, 1, 3, 1, 1, 2, 3, 1, 2, 1, 4, 2, 4, 1, 4, 2, 2, 3, 1, 1, 1, 3, 1, 2, 2, 3, 2, 2, 7, 1, 1, 1, 5, 1, 1, 2, 2, 4, 1, 1, 1, 1, 2, 1, 2, 3, 1, 1, 4, 1, 1, 3, 3, 3, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 6, 4, 2, 1, 4, 1, 1, 4, 2, 4, 1, 1, 1, 1, 3, 1, 2, 1, 1, 3, 1, 5, 1, 7, 1, 1, 1, 1, 1, 8, 3, 1, 2, 3, 4, 1, 1, 1, 1

Offset: 1

Antti Karttunen, Oct 03 2019

nonn

First differences of A327985, which gives indices of zeros in A051023.

			The evolution of one-dimensional cellular automaton rule 30 proceeds as follows, when started from a single alive (1) cell:
   0:              (1)
   1:             1(1)1
   2:            11(0)01
   3:           110(1)111
   4:          1100(1)0001
   5:         11011(1)10111
   6:        110010(0)001001
   7:       1101111(0)0111111
   8:      11001000(1)11000001
   9:     110111101(1)001000111
  10:    1100100001(0)1111011001
  11:   11011110011(0)10000101111
  12:  110010001110(0)110011010001
When noting up the distances between successive 0's in its central column (indicated here with parentheses), we obtain 6-2 (as the first 0 is on row 2, and the second is on row 6), 7-6, 10-7, 11-10, 12-11, ..., that is, the first terms of this sequence: 4, 1, 3, 1, 1, ...

Antti Karttunen, Table of n, a(n) for n = 1..100000
Index entries for sequences related to cellular automata

Cf. A051023, A110240, A245549, A269160, A327981, A327983, A327985.

A327980list[upto_]:=Differences[Flatten[Position[CellularAutomaton[30,{{1},0},{upto,{{0}}}],0]]];A327980list[300] (* Paolo Xausa, Jun 01 2023 *)

up_to = 105;
A269160(n) = bitxor(n, bitor(2*n, 4*n));
A327980list(up_to) = { my(v=vector(up_to), s=25, n=2, on=n, k=0); while(kA269160(s); if(!((s>>n)%2), k++; v[k] = (n-on); on=n)); (v); }
v327980 = A327980list(up_to);
A327980(n) = v327980[n];

a(n) = A327985(1+n) - A327985(n).

A265156 Decimal representation of the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 0, 21, 0, 381, 136, 5189, 544, 94493, 43176, 1311749, 254944, 24400989, 10617384, 336720133, 59386080, 6262162781, 2688081960, 86425034501, 15602819808, 1602324730205, 689510189096, 22111597905669, 4029655427808, 410123492458845, 176987155003432, 5661487452198661, 1029729726008032, 104994856690270557, 45284638610044968

Offset: 0

Robert Price, Dec 02 2015

			From _Michael De Vlieger_, Dec 04 2015: (Start)
First 12 rows, showing surrounding context at left, cells generated by the initial cell at center, and the decimal equivalent at right where leading zeros are lost:
0                           1                         ->         1
1                         0 0 0                       ->         0
0                       1 0 1 0 1                     ->        21
1                     0 0 0 0 0 0 0                   ->         0
0                   1 0 1 1 1 1 1 0 1                 ->       381
1                 0 0 0 1 0 0 0 1 0 0 0               ->       136
0               1 0 1 0 0 0 1 0 0 0 1 0 1             ->      5189
1             0 0 0 0 0 1 0 0 0 1 0 0 0 0 0           ->       544
0           1 0 1 1 1 0 0 0 1 0 0 0 1 1 1 0 1         ->     94493
1         0 0 0 1 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0       ->     43176
0       1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 1 0 1     ->   1311749
1     0 0 0 0 0 1 1 1 1 1 0 0 0 1 1 1 1 1 0 0 0 0 0   ->    254944
0   1 0 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 0 1 0 1 1 1 0 1 ->  24400989
(End)

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A245549, A262448, A265122.

rule = 73; rows = 30; Table[FromDigits[Table[Take[CellularAutomaton[rule,{{1},0}, rows-1, {All,All}][[k]], {rows-k+1, rows+k-1}], {k,1,rows}][[k]],2], {k,1,rows}]

A265205 Number of ON (black) cells in the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 0, 3, 0, 7, 2, 5, 2, 9, 6, 5, 10, 13, 6, 11, 10, 15, 10, 19, 10, 23, 10, 17, 20, 19, 16, 25, 18, 19, 20, 25, 14, 37, 20, 27, 26, 35, 20, 37, 30, 41, 24, 33, 36, 39, 26, 45, 36, 37, 38, 41, 36, 49, 44, 29, 56, 39, 40, 57, 40, 43, 60, 39, 48, 55, 44, 45, 64

Offset: 0

Robert Price, Dec 04 2015

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A245549, A262448, A265122, A265156.

rule = 73; 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}]

A265206 Total number of ON (black) cells after n iterations of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 1, 4, 4, 11, 13, 18, 20, 29, 35, 40, 50, 63, 69, 80, 90, 105, 115, 134, 144, 167, 177, 194, 214, 233, 249, 274, 292, 311, 331, 356, 370, 407, 427, 454, 480, 515, 535, 572, 602, 643, 667, 700, 736, 775, 801, 846, 882, 919, 957, 998, 1034, 1083, 1127, 1156

Offset: 0

Robert Price, Dec 04 2015

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A245549, A262448, A265122, A265156, A265205.

rule = 73; rows = 30; Table[Total[Take[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}],k]],{k,1,rows}]

A265219 Number of OFF (white) cells in the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

0, 3, 2, 7, 2, 9, 8, 13, 8, 13, 16, 13, 12, 21, 18, 21, 18, 25, 18, 29, 18, 33, 28, 27, 30, 35, 28, 37, 38, 39, 36, 49, 28, 47, 42, 45, 38, 55, 40, 49, 40, 59, 52, 51, 50, 65, 48, 59, 60, 61, 60, 67, 56, 63, 80, 55, 74, 75, 60, 79, 78, 63, 86, 79, 74, 87, 88

Offset: 0

Robert Price, Dec 05 2015

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A245549, A262448, A265122, A265156, A265205, A265206.

A261299 Binary representation of the middle column of the "Rule 30" elementary cellular automaton starting with a single ON (black) cell.

Original entry on oeis.org

1, 11, 110, 1101, 11011, 110111, 1101110, 11011100, 110111001, 1101110011, 11011100110, 110111001100, 1101110011000, 11011100110001, 110111001100010, 1101110011000101, 11011100110001011, 110111001100010110, 1101110011000101100, 11011100110001011001

Offset: 0

Robert Price, Dec 05 2015

S. Wolfram, A New Kind of Science, Wolfram Media, 2002; p. 55.

Robert Price, Table of n, a(n) for n = 0..999
Eric Weisstein's World of Mathematics, Elementary Cellular Automaton
Index entries for sequences related to cellular automata
Index to Elementary Cellular Automata

Cf. A070950, A245549, A110240, A051023, A092539, A070952, A110267.

A261299list[nmax_]:=With[{ca=CellularAutomaton[30,{{1},0},{nmax,{{0}}}]},Array[FromDigits[Take[ca,#]]&,nmax+1]];A261299list[25] (* Paolo Xausa, May 30 2023 *)

cp's OEIS Frontend

A110240 Decimal form of binary integer produced by the ON cells at n-th generation following Wolfram's Rule 30 cellular automaton starting from a single ON-cell represented as 1.

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A070950 Triangle read by rows giving successive states of cellular automaton generated by "Rule 30".

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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.

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A265122 Binary representation of the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

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A327980 Distances between successive zeros in A051023, the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

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A265156 Decimal representation of the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

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A265205 Number of ON (black) cells in the n-th iteration of the "Rule 73" elementary cellular automaton starting with a single ON (black) cell.

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