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

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