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
KEYWORD
nonn,easy,changed
AUTHOR
Clark Kimberling, Nov 10 2012
STATUS
approved