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A004697
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a(n) = floor(Fibonacci(n)/4).
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4
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0, 0, 0, 0, 0, 1, 2, 3, 5, 8, 13, 22, 36, 58, 94, 152, 246, 399, 646, 1045, 1691, 2736, 4427, 7164, 11592, 18756, 30348, 49104, 79452, 128557, 208010, 336567, 544577, 881144, 1425721, 2306866, 3732588, 6039454
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OFFSET
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0,7
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COMMENTS
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LINKS
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FORMULA
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G.f.: x^5 / ((1-x)*(1-x-x^2)*(1+x^2+x^4)).
a(n) = floor(Fibonacci(n)/4).
a(n) = ceiling(Fibonacci(n)/4-3/4).
a(n) = round(Fibonacci(n)/4-3/8).
a(n) = Sum_{k=1..n-2} round(Fibonacci(n)/4).
a(n) = a(n-6) + Fibonacci(n-3), n > 5. (End)
a(n) = 2*a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) - a(n-7). - R. J. Mathar, Jan 08 2011
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MAPLE
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A004697 := proc(n) floor(combinat[fibonacci](n)/4) ; end proc:
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MATHEMATICA
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CoefficientList[Series[x^5/((1-x)*(1-x-x^2)*(1+x^2+x^4)), {x, 0, 50}], x] (* Vincenzo Librandi, Jul 09 2012 *)
Floor[Fibonacci[Range[0, 50]]/4] (* or *) LinearRecurrence[ {2, -1, 1, -1, 1, 0, -1}, {0, 0, 0, 0, 0, 1, 2}, 50] (* Harvey P. Dale, Dec 05 2012 *)
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PROG
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(PARI) vector(50, n, n--; fibonacci(n)\4) \\ G. C. Greubel, Oct 09 2018
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CROSSREFS
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See A000045 for the Fibonacci numbers.
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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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