A215091 - OEIS

%I #6 Oct 27 2015 14:20:23

%S 2,5,11,25,55,123,275,615,1375,3075,6875,15373,34375,76865,171875,

%T 384325,859376,1921624,4296881,9608119,21484407,48040595,107422036,

%U 240202975,537110180,1201014874,2685550900,6005074370,13427754501

%N Power floor-ceiling sequence of sqrt(5).

%C 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...

%H Clark Kimberling, <a href="/A215091/b215091.txt">Table of n, a(n) for n = 0..250</a>

%F 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).

%e a(0) = floor(r) = 2 , where r = sqrt(5);

%e a(1) = ceiling(2*r) = 5; a(2) = floor(5*r ) = 11.

%t (See A214999.)

%t 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 *)

%Y Cf. A214992, A214999, A218982, A218983.

%K nonn,easy

%O 0,1

%A _Clark Kimberling_, Nov 10 2012