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0, 0, 2, 2, 2, 4, 6, 4, 8, 10, 10, 8, 12, 8, 18, 6, 12, 26, 16, 18, 14, 18, 20, 22, 22, 26, 26, 38, 30, 26, 36, 26, 28, 36, 28, 18, 28, 42, 36, 32, 34, 40, 44, 38, 40, 50, 48, 48, 50, 58, 46, 56, 48, 42, 54, 48, 56, 56, 46, 54, 48, 52, 60, 58, 78, 74, 64, 60, 66, 74, 74, 64, 80, 74, 80, 62, 92, 62, 80, 70, 68, 100, 90, 82, 80, 92
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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COMMENTS
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a(n) is the number of times the k-th cell from the left is different from the k-th cell from the right, at the generation n of Rule 30 1-D cellular automaton, when it is started from a single alive cell.
All terms are even.
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LINKS
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FORMULA
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EXAMPLE
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The evolution of one-dimensional cellular automaton rule 30 proceeds as follows, when started from a single alive (1) cell:
---------------------------------------------- a(n)
0: (1) 0
1: 1(1)1 0
2: 11(0)01 2
3: 110(1)111 2
4: 1100(1)0001 2
5: 11011(1)10111 4
6: 110010(0)001001 6
7: 1101111(0)0111111 4
8: 11001000(1)11000001 8
9: 110111101(1)001000111 10
10: 1100100001(0)1111011001 10
11: 11011110011(0)10000101111 8
12: 110010001110(0)110011010001 12
13: 1101111011001(1)1011100110111 8
When we count the times the k-th cell from the left is different from the k-th cell from the right, we obtain a(n). Note that the central cells (indicated with parentheses) do not affect the count, as the central cell is always equal to itself.
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PROG
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(PARI)
A030101(n) = if(n<1, 0, subst(Polrev(binary(n)), x, 2));
\\ Use this one for writing b-files:
A328106write(up_to) = { my(s=1, n=0); for(n=0, up_to, write("b328106.txt", n, " ", hammingweight(bitxor(s, A030101(s)))); s = A269160(s)); };
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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