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 A183136 #26 Jun 21 2025 11:17:21 %S A183136 0,1,2,4,7,10,14,18,23,29,35,42,50,58,67,76,86,97,108,120,132,145,159, %T A183136 173,188,204,220,237,254,272,291,310,330,351,372,394,416,439,463,487, %U A183136 512,537,563,590,617,645,674,703,733,763,794,826,858 %N A183136 a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor. %C A183136 a(n) + A183137(n) = A000217(n) (the triangular numbers). %H A183136 Paolo Xausa, <a href="/A183136/b183136.txt">Table of n, a(n) for n = 1..10000</a> %H A183136 Hector Zenil, N. Kiani, and J. Tegner, <a href="https://arxiv.org/abs/1608.05972">Low Algorithmic Complexity Entropy-deceiving Graphs</a>, arXiv preprint arXiv:1608.05972 [cs.IT], 2016-2017. %F A183136 a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor. %e A183136 The terms [k/r] are given by A060143 (and A005206): 0,1,1,2,3,3,4,4,5,6,6,7,8,8,... %t A183136 Accumulate[Floor[Range[100]/GoldenRatio]] (* _Paolo Xausa_, Jun 20 2025 *) %o A183136 (PARI) default(realprecision,100); r=(1+sqrt(5))/2; for(n=1,99, print1(sum(k=1,n,floor(k/r)), ", ")) %o A183136 (Python) %o A183136 from math import isqrt %o A183136 def A183136(n): return sum(isqrt(5*i**2)-i>>1 for i in range(1,n+1)) # _Chai Wah Wu_, Jun 20 2025 %Y A183136 Cf. A183137, A000217, A005206, A060143, A060144. %K A183136 nonn %O A183136 1,3 %A A183136 _Clark Kimberling_, Dec 26 2010