%I #9 Oct 04 2019 23:30:38

%S 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,

%T 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,

%U 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

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

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

%H Antti Karttunen, <a href="/A328102/b328102.txt">Table of n, a(n) for n = 1..100000</a>

%H <a href="/index/Ce#cell">Index entries for sequences related to cellular automata</a>

%H <a href="/index/Ch#char_fns">Index entries for characteristic functions</a>

%F a(n) = A000035(floor(A110240(n) / 2^(n+1))).

%F a(n) = A000035(floor(A265281(n) / 2^(n-1))).

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

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

%e ---------------------------------------------- a(n)

%e 0: 1

%e 1: (1)11 1

%e 2: 1(1)001 1

%e 3: 11(0)1111 0

%e 4: 110(0)10001 0

%e 5: 1101(1)110111 1

%e 6: 11001(0)0001001 0

%e 7: 110111(1)00111111 1

%e 8: 1100100(0)111000001 0

%e 9: 11011110(1)1001000111 1

%e 10: 110010000(1)01111011001 1

%e 11: 1101111001(1)010000101111 1

%e 12: 11001000111(0)0110011010001 0

%e 13: 110111101100(1)11011100110111 1

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

%t Rest@ CellularAutomaton[30, {{1}, 0}, {106, {{-1}}}] (* _Michael De Vlieger_, Oct 04 2019 *)

%o (PARI)

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

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

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

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

%o 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)); };

%o (PARI)

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

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

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

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

%Y Cf. also A051023, A328101.

%K nonn

%O 1

%A _Antti Karttunen_, Oct 04 2019