Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 May 12 2024 15:25:01
%S 0,1,2,2,4,4,5,6,6,8,8,9,10,11,11,13,12,15,14,16,16,17,18,19,19,21,21,
%T 22,23,23,25,25,26,27,28,28,30,29,32,31,33,33,34,35,36,36,38,38,39,40,
%U 40,42,42,43,44,44,46,46,47,48,49,49,51,50,53,52,54,54,56,55,58,56,60,58
%N a(n) = floor(n*r)-a(n-1), where r is the golden mean, (1+sqrt(5))/2.
%C a(2n+2) - a(2n) = A339824(n), since a(2n+2) - a(2n) = a(2n+2) + a(2n+1) - a(2n+1) - a(2n) = floor((2n+2)r) - floor((2n+1)r). - _Michel Dekking_, Feb 23 2021
%H Paolo Xausa, <a href="/A129229/b129229.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = floor(n*r)-floor((n-1)*r)+floor((n-2)*r)-...+d*floor(r), where d=(-1)^(n+1) and r = (1+sqrt(5))/2.
%F a(n) + a(n-1) = floor(n*r). - _Michel Dekking_, Feb 23 2021
%t nxt[{n_,a_}]:={n+1,Floor[GoldenRatio(n+1)]-a}; Transpose[NestList[nxt,{0,0},80]][[2]] (* _Harvey P. Dale_, Dec 08 2015 *)
%t Block[{n = 0}, NestList[Floor[++n*GoldenRatio] - # &, 0, 100]] (* _Paolo Xausa_, May 12 2024 *)
%Y Cf. A001622, A129230, A129231, A087851, A339824, A339825.
%K nonn
%O 0,3
%A _Clark Kimberling_, Apr 04 2007