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

Author

Clark Kimberling, Nov 10 2012

Keywords

• nonn
• easy

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...

Examples

			a(0) = floor(r) = 2, where r = sqrt(5);
a(1) = ceiling(2*r) = 5; a(2) = floor(5*r) = 11.
		

Links

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

Crossrefs

Cf. A214992, A214999, A218982, A218983.

Programs

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 *)

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).