A328100 Column which is two positions right of the middle column of rule-30 1-D cellular automaton, when started from a lone 1 cell.

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

Offset

2

Comments

Equally, column which is two steps 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 = 2..100000

Index entries for sequences related to cellular automata

Index entries for characteristic functions

Formula

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

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

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:             111
   2:            1100(1)                        1
   3:           11011(1)1                       1
   4:          110010(0)01                      0
   5:         1101111(0)111                     0
   6:        11001000(0)1001                    0
   7:       110111100(1)11111                   1
   8:      1100100011(1)000001                  1
   9:     11011110110(0)1000111                 0
  10:    110010000101(1)11011001                1
  11:   1101111001101(0)000101111               0
  12:  11001000111001(1)0011010001              1
  13: 110111101100111(0)11100110111             0
For this sequence, we pick the bit two positions right of the center (marked here with parentheses).

Mathematica

Drop[CellularAutomaton[30, {{1}, 0}, {107, {{2}}}] , 2] (* 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)));
A328100(n) = ((A110240(n)>>(n-2))%2);
\\ Use this one if writing directly to a file:
A328100write(up_to) = { my(s=1, n=0); for(n=0, up_to, if(n>=2, write("b328100.txt", n, " ", ((s>>(n-2))%2))); s = A269160(s)); };
(PARI)
A269161(n) = bitxor(4*n, bitor(2*n, n));
A265281(n) = if(!n, 1, A269161(A265281(n-1)));
A328100(n) = ((A265281(n)>>(n+2))%2);

Crossrefs

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

Cf. also A051023, A328101, A328102.

Sequence in context: A085002 A170966 A190245 * A332479 A362460 A190210

Adjacent sequences: A328097 A328098 A328099 * A328101 A328102 A328103

Keyword

nonn

Author

Antti Karttunen, Oct 04 2019

Status

approved