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A215091
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Power floor-ceiling sequence of sqrt(5).
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5
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2, 5, 11, 25, 55, 123, 275, 615, 1375, 3075, 6875, 15373, 34375, 76865, 171875, 384325, 859376, 1921624, 4296881, 9608119, 21484407, 48040595, 107422036, 240202975, 537110180, 1201014874, 2685550900, 6005074370, 13427754501
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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 floor-ceiling sequence and the power floor-ceiling function, p2(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = sqrt(5), and the limit p2(r) = 2.20000329748317471983660768168522753590...
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LINKS
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FORMULA
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a(n) = ceiling(x*a(n-1)) if n is odd, a(n) = floor(x*a(n-1) if n is even, where x = sqrt(5) and a(0) = floor(x).
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EXAMPLE
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a(0) = floor(r) = 2 , where r = sqrt(5);
a(1) = ceiling(2*r) = 5; a(2) = floor(5*r ) = 11.
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MATHEMATICA
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nxt[{n_, a_}]:={n+1, If[OddQ[n], Floor[Sqrt[5]*a], Ceiling[Sqrt[5]*a]]}; Transpose[ NestList[nxt, {0, 2}, 30]][[2]] (* Harvey P. Dale, Oct 27 2015 *)
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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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