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A218982
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Power ceiling-floor sequence of sqrt(5).
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5
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3, 6, 14, 31, 70, 156, 349, 780, 1745, 3901, 8723, 19505, 43615, 97526, 218075, 487630, 1090374, 2438150, 5451870, 12190751, 27259348, 60953755, 136296740, 304768775, 681483699, 1523843876, 3407418494, 7619219380, 17037092470
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OFFSET
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0,1
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COMMENTS
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See A214992 for a discussion of power ceiling-floor sequence and power ceiling-floor function, p3(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = sqrt(5), and the limit p3(r) = 2.79135723025040661923369247589566824549062...
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LINKS
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FORMULA
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a(n) = floor(x*a(n-1)) if n is odd, a(n) = ceiling(x*a(n-1) if n is even, where x=sqrt(5) and a(0) = ceiling(x).
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EXAMPLE
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a(0) = ceiling(r) = 3 , where r = sqrt(5);
a(1) = floor(3*r) = 6; a(2) = ceiling(6*r ) = 14.
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MATHEMATICA
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CROSSREFS
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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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