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Search: id:A092550
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| A092550 |
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A two steps forward and one step back Fibonacci based switched sequence inspired by Per Bak's sand piles. |
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+0
2
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| 1, 1, 1, 2, 3, 2, 5, 7, 5, 12, 17, 12, 29, 41, 29, 70, 99, 70, 169, 239, 169, 408, 577, 408, 985, 1393, 985, 2378, 3363, 2378, 5741, 8119, 5741, 13860, 19601, 13860, 33461, 47321, 33461, 80782, 114243, 80782, 195025, 275807, 195025, 470832, 665857
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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m=2 gives an addition sequence alternating ones, but all the sequences of m to m=10 seem to give new sequences. It seems a comment on human history in its cycles. I was inspired by Per Bak, but his definition is a random/ probabilistic one for sand pile collapse: here the collapse is sure and has a definite cycle length.
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FORMULA
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a[n] =If[Mod[n, m]==0, a[n-2], a[n-1]+a[n-2]]
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MATHEMATICA
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m=3 fib[n_Integer?Positive] :=fib[n] =If[Mod[n, m]==0, fib[n-2], fib[n-1]+fib[n-2]] fib[0]=fib[1] = fib[2] = 1 digits=50 a=Table[fib[n], {n, 1, digits}]
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CROSSREFS
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Cf. A000045.
Sequence in context: A133684 A025473 A092556 this_sequence A058977 A085818 A064939
Adjacent sequences: A092547 A092548 A092549 this_sequence A092551 A092552 A092553
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2004
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