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A093148
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a(n) = gcd(Fibonacci(n+5), Fibonacci(n+1)).
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7
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1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 3, 1
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listen;
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internal format)
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OFFSET
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0,4
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COMMENTS
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Periodic sequence: Repeat [1, 1, 1, 3].
Continued fraction expansion of (9+sqrt(165))/14.
Decimal expansion of 371/3333. (End)
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LINKS
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FORMULA
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G.f.: (1+x+x^2+3*x^3)/(1-x^4); a(n) = 3/2-sin(Pi*n/2)-cos(Pi*n)/2.
a(n) = a(n-4) for n > 3; a(0) = a(1) = a(2) = 1, a(3) = 3.
a(n) = (3-(-1)^n+(1-(-1)^n)*i*i^n)/2 where i = sqrt(-1). (End)
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MAPLE
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MATHEMATICA
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f[n_] := Switch[Mod[n, 4], 0, 1, 1, 1, 2, 1, 3, 3]; Array[f, 105, 0] (* Robert G. Wilson v, Jan 23 2012 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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