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A363343
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Array read by ascending antidiagonals: T(n,k) is the value of the k-th cell on the n-th diagonal from the right of rule-30 1-D cellular automaton, when started from a single ON cell, with n, k >= 1.
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6
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1, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 1, 1, 0, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 0, 0, 1, 0, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1
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OFFSET
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1
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COMMENTS
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Diagonals from the right are periodic, with periods (A094605) being a power of 2 and doubling at apparently non-predictable intervals.
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LINKS
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Eric Weisstein's World of Mathematics, Rule 30.
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EXAMPLE
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The following diagram illustrates how the array is built.
.
1
\
1 1 1
\ \ \
1 1 0 0 1
\ \ \ \ \
1 1 0 1 1 1 1
\ \ \ \ \ \
1 1 0 0 1 0 0 0 1
\ \ \ \ \ \
1 1 0 1 1 1 1 0 1 1 1 Array begins:
\ \ \ \ \ \___ 1 1 1 1 1 1 1 1 1 1 1 1 ... (period 1)
... \ \ \ \ \____ 1 0 1 0 1 0 1 0 1 0 1 0 ... (period 2)
\ \ \ \_____ 1 0 1 0 1 0 1 0 1 0 1 0 ... (period 2)
\ \ \______ 1 1 0 0 1 1 0 0 1 1 0 0 ... (period 4)
\ \_______ 1 0 1 1 0 1 0 0 1 0 1 1 ... (period 8)
\________ 1 0 1 0 1 0 0 0 1 0 1 0 ... (period 8)
...
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MATHEMATICA
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A363343list[dmax_]:=Module[{ca=CellularAutomaton[30, {{1}, 0}, dmax-1], a}, a=Array[Drop[Diagonal[ca, #], Floor[(dmax-#)/2]]&, dmax, 0]; Array[Diagonal[a, #]&, dmax, 1-dmax]]; A363343list[15] (* Generates 15 antidiagonals *)
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CROSSREFS
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Cf. A094605 (periods of diagonals), A363344 (diagonals from the left).
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KEYWORD
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AUTHOR
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STATUS
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approved
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