This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A215091 #9 Oct 29 2024 09:09:38
%S A215091 2,5,11,25,55,123,275,615,1375,3075,6875,15373,34375,76865,171875,
%T A215091 384325,859376,1921624,4296881,9608119,21484407,48040595,107422036,
%U A215091 240202975,537110180,1201014874,2685550900,6005074370,13427754501
%N A215091 Power floor-ceiling sequence of sqrt(5).
%C A215091 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 A215091 Clark Kimberling, <a href="/A215091/b215091.txt">Table of n, a(n) for n = 0..250</a>
%F A215091 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 A215091 a(0) = floor(r) = 2, where r = sqrt(5);
%e A215091 a(1) = ceiling(2*r) = 5; a(2) = floor(5*r) = 11.
%t A215091 (See A214999.)
%t A215091 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 A215091 Cf. A214992, A214999, A218982, A218983.
%K A215091 nonn,easy
%O A215091 0,1
%A A215091 _Clark Kimberling_, Nov 10 2012