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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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1
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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; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| 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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REFERENCES
| Marcia Edson, Scott Lewis and Omer Yayenie, THE K-PERIODIC FIBONACCI SEQUENCE AND AN EXTENDED BINET'S FORMULA, INTEGERS 11 (2011) #A32.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (0,0,2,0,0,1).
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FORMULA
| a(n) = a(n-2) if 3|n, otherwise a(n)= a(n-1)+a(n-2).
a(n)= +2*a(n-3) +a(n-6). G.f. -x*(1+x+x^2+x^4)/(-1+2*x^3+x^6). [R. J. Mathar, Dec 08 2010]
a(3n+1) = A000129(n+1). a(3n)=A000129(n). a(3n+2)= A078057(n). [R. J. Mathar, Dec 08 2010]
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MATHEMATICA
| 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
| Cf. A000045.
Sequence in context: A025473 A192141 A092556 * A058977 A085818 A064939
Adjacent sequences: A092547 A092548 A092549 * A092551 A092552 A092553
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 08 2004
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