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A215091 Power floor-ceiling sequence of sqrt(5). 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

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...

LINKS

Clark Kimberling, Table of n, a(n) for n = 0..250

FORMULA

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).

EXAMPLE

a(0) = floor(r) = 2 , where r = sqrt(5);

a(1) = ceiling(2*r) = 5; a(2) = floor(5*r ) = 11.

MATHEMATICA

(See A214999.)

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 *)

CROSSREFS

Cf. A214992, A214999, A218982, A218983.

Sequence in context: A172481 A151529 A192922 * A017919 A017920 A228765

Adjacent sequences:  A215088 A215089 A215090 * A215092 A215093 A215094

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Nov 10 2012

STATUS

approved

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Last modified May 18 10:19 EDT 2021. Contains 343995 sequences. (Running on oeis4.)