A215091 - OEIS

A215091

Power floor-ceiling sequence of sqrt(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

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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.