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

0,1

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...

Links

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

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).

Example

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

Mathematica

(See A214999.)

Crossrefs

Cf. A214992, A214999, A215091, A218983.

Sequence in context: A091601 A339154 A063119 * A106803 A199853 A006356

Adjacent sequences: A218979 A218980 A218981 * A218983 A218984 A218985

Keyword

nonn,easy

Author

Clark Kimberling, Nov 10 2012

Status

approved