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Search: id:A106293
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| 1, 1, 13, 4, 31, 13, 48, 8, 39, 31, 10, 52, 168, 48, 403, 16, 96, 39, 360, 124, 624, 10, 553, 104, 155, 168, 117, 48, 140, 403, 331, 32, 130, 96, 1488, 156, 469, 360, 2184, 248, 560, 624, 308, 20, 1209, 553, 46, 208, 336, 155, 1248, 168, 52, 117, 310, 48, 4680, 140
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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This sequence differs from the corresponding Fibonacci sequence (A046738) at all n that are multiples of 2 or 11 because the discriminant of the characteristic polynomial x^3-x^2-x-1 is -44.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein's World of Mathematics, Fibonacci n-Step
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FORMULA
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Let the prime factorization of n be p1^e1...pk^ek. Then a(n) = lcm(a(p1^e1), ..., a(pk^ek)).
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MATHEMATICA
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n=3; Table[p=i; a=Join[Table[ -1, {n-1}], {n}]; a=Mod[a, p]; a0=a; k=0; While[k++; s=Mod[Plus@@a, p]; a=RotateLeft[a]; a[[n]]=s; a!=a0]; k, {i, 60}]
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CROSSREFS
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Cf. A046738 (period of Fibonacci 3-step sequence mod n), A106273 (discriminant of the polynomial x^n-x^(n-1)-...-x-1).
Sequence in context: A155847 A010219 A056139 this_sequence A046734 A123172 A010218
Adjacent sequences: A106290 A106291 A106292 this_sequence A106294 A106295 A106296
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), May 02 2005
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