A218982 Power ceiling-floor sequence of sqrt(5).

3, 6, 14, 31, 70, 156, 349, 780, 1745, 3901, 8723, 19505, 43615, 97526, 218075, 487630, 1090374, 2438150, 5451870, 12190751, 27259348, 60953755, 136296740, 304768775, 681483699, 1523843876, 3407418494, 7619219380, 17037092470

Offset: 0

Author

Clark Kimberling, Nov 10 2012

Keywords

• nonn
• easy

Comments

See A214992 for a discussion of power ceiling-floor sequence and power ceiling-floor function, p3(x) = limit of a(n,x)/x^n. The present sequence is a(n,r), where r = sqrt(5), and the limit p3(r) = 2.79135723025040661923369247589566824549062...

Examples

			a(0) = ceiling(r) = 3, where r = sqrt(5);
a(1) = floor(3*r) = 6; a(2) = ceiling(6*r) = 14.
		

Links

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

Crossrefs

Cf. A214992, A214999, A215091, A218983.

Programs

Mathematica

(See A214999.)

Formula

a(n) = floor(x*a(n-1)) if n is odd, a(n) = ceiling(x*a(n-1)) if n is even, where x=sqrt(5) and a(0) = ceiling(x).