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A287576
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Start with 0 and repeatedly substitute 0->0321, 1->3210, 2->2103, 3->1032.
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6
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0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 1, 0, 3, 2, 2, 1, 0, 3, 3, 2, 1, 0, 0, 3, 2, 1, 0, 3, 2, 1, 1, 0
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OFFSET
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1,2
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COMMENTS
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This is the fixed point of the morphism 0->0231, 1->2310, 2->3102, 3->1023 starting with 0. Let t be the (nonperiodic) sequence of positions of 0, and likewise, u for 1, v for 2, and w for 3; then t(n)/n -> 4, u(n)/n -> 4, v(n)/n -> 4, w(n)/n -> 4. Also, t(n) + u(n) + v(n) + w(n) = 16*n - 6 for n >= 1. See A287556 for a guide to related sequences.
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LINKS
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FORMULA
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EXAMPLE
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First three iterations of the morphism:
0321
0321103221033210
0321103221033210321003211032210321033210032110321032210332100321
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MATHEMATICA
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s = Nest[Flatten[# /. {0 -> {0, 3, 2, 1}, 1 -> {3, 2, 1, 0}, 2 -> {2, 1, 0, 3}, 3 -> {1, 0, 3, 2}}] &, {0}, 9]; (* A287576 *)
Flatten[Position[s, 0]]; (* A287577 *)
Flatten[Position[s, 1]]; (* A287578 *)
Flatten[Position[s, 2]]; (* A287579 *)
Flatten[Position[s, 3]]; (* A287580 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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