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A183136 a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor. 4

%I #14 Aug 18 2017 09:42:27

%S 0,1,2,4,7,10,14,18,23,29,35,42,50,58,67,76,86,97,108,120,132,145,159,

%T 173,188,204,220,237,254,272,291,310,330,351,372,394,416,439,463,487,

%U 512,537,563,590,617,645,674,703,733,763,794,826,858

%N a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.

%C a(n) + A183137(n) = A000217(n) (the triangular numbers).

%H Hector Zenil, N. Kiani, 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.

%F a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.

%e The terms [k/r] are given by A060143 (and A005206): 0,1,1,2,3,3,4,4,5,6,6,7,8,8,...

%o (PARI) default(realprecision,100); r=(1+sqrt(5))/2; for(n=1,99, print1(sum(k=1,n,floor(k/r)), ", "))

%Y Cf. A183137, A000217, A005206, A060143, A060144.

%K nonn

%O 1,3

%A _Clark Kimberling_, Dec 26 2010

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Last modified April 24 20:08 EDT 2024. Contains 371963 sequences. (Running on oeis4.)