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A328101 Column immediately right of the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell. 4
1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 0, 0, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1, 0, 0, 1, 1, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 1, 0, 1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

1

COMMENTS

Equally, column immediately left of the middle column of rule-86 1-D cellular automaton, when started from a lone 1 cell.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..100000

Index entries for sequences related to cellular automata

Index entries for characteristic functions

FORMULA

a(n) = A000035(floor(A110240(n) / 2^(n-1))).

a(n) = A000035(floor(A265281(n) / 2^(n+1))).

EXAMPLE

The evolution of one-dimensional cellular automaton rule 30 proceeds as follows, when started from a single alive (1) cell:

---------------------------------------------- a(n)

   0:              1

   1:             11(1)                         1

   2:            110(0)1                        0

   3:           1101(1)11                       1

   4:          11001(0)001                      0

   5:         110111(1)0111                     1

   6:        1100100(0)01001                    0

   7:       11011110(0)111111                   0

   8:      110010001(1)1000001                  1

   9:     1101111011(0)01000111                 0

  10:    11001000010(1)111011001                1

  11:   110111100110(1)0000101111               1

  12:  1100100011100(1)10011010001              1

  13: 11011110110011(1)011100110111             1

For this sequence, we pick the bit immediately right of the center (marked here with parentheses).

MATHEMATICA

Rest@ CellularAutomaton[30, {{1}, 0}, {106, {{1}}}] (* Michael De Vlieger, Oct 04 2019 *)

PROG

(PARI)

A269160(n) = bitxor(n, bitor(2*n, 4*n)); \\ From A269160.

A110240(n) = if(!n, 1, A269160(A110240(n-1)));

A328101(n) = ((A110240(n)>>(n-1))%2);

\\ Use this one if writing directly to a file:

A328101write(up_to) = { my(s=1, n=0); for(n=0, up_to, if(n>=1, write("b328101.txt", n, " ", ((s>>(n-1))%2))); s = A269160(s)); };

(PARI)

A269161(n) = bitxor(4*n, bitor(2*n, n));

A265281(n) = if(!n, 1, A269161(A265281(n-1)));

A328101(n) = ((A265281(n)>>(n+1))%2);

CROSSREFS

Cf. A000035, A110240, A269160, A269161, A265281.

Cf. also A051023, A328100, A328102.

Sequence in context: A267513 A004569 A100060 * A147850 A286046 A189215

Adjacent sequences:  A328098 A328099 A328100 * A328102 A328103 A328104

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 04 2019

STATUS

approved

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)