A328102 - OEIS

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A328102

Column immediately left of the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

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

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OFFSET

COMMENTS

Equally, column immediately right 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))).

a(n) = A051023(1+n) XOR (A051023(n) or A328101(n)).

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: (1)11 1

2: 1(1)001 1

3: 11(0)1111 0

4: 110(0)10001 0

5: 1101(1)110111 1

6: 11001(0)0001001 0

7: 110111(1)00111111 1

8: 1100100(0)111000001 0

9: 11011110(1)1001000111 1

10: 110010000(1)01111011001 1

11: 1101111001(1)010000101111 1

12: 11001000111(0)0110011010001 0

13: 110111101100(1)11011100110111 1

For this sequence, we pick the bit immediately left 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)));

A328102(n) = ((A110240(n)>>(n+1))%2);

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

A328102write(up_to) = { my(s=1, n=0); for(n=0, up_to, if(n>=1, write("b328102.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)));

A328102(n) = ((A265281(n)>>(n-1))%2);

CROSSREFS

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

Cf. also A051023, A328101.

Sequence in context: A359377 A353663 A260595 * A177444 A325896 A239200

Adjacent sequences: A328099 A328100 A328101 * A328103 A328104 A328105

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 04 2019

STATUS

approved