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A183136
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a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.
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4
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0, 1, 2, 4, 7, 10, 14, 18, 23, 29, 35, 42, 50, 58, 67, 76, 86, 97, 108, 120, 132, 145, 159, 173, 188, 204, 220, 237, 254, 272, 291, 310, 330, 351, 372, 394, 416, 439, 463, 487, 512, 537, 563, 590, 617, 645, 674, 703, 733, 763, 794, 826, 858
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OFFSET
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1,3
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COMMENTS
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a(n) + A183137(n) = A000217(n) (the triangular numbers).
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LINKS
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Table of n, a(n) for n=1..53.
Hector Zenil, N. Kiani, J. Tegner, Low Algorithmic Complexity Entropy-deceiving Graphs, arXiv preprint arXiv:1608.05972 [cs.IT], 2016.
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FORMULA
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a(n) = [1/r]+[2/r]+...+[n/r], where r = golden ratio = (1+sqrt(5))/2 and []=floor.
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EXAMPLE
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The terms [k/r] are given by A060143 (and A005206): 0,1,1,2,3,3,4,4,5,6,6,7,8,8,...
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PROG
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(PARI) default(realprecision, 100); r=(1+sqrt(5))/2; for(n=1, 99, print1(sum(k=1, n, floor(k/r)), ", "))
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CROSSREFS
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Cf. A183137, A000217, A005206, A060143, A060144.
Sequence in context: A014616 A184674 A227353 * A144873 A120679 A145106
Adjacent sequences: A183133 A183134 A183135 * A183137 A183138 A183139
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KEYWORD
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nonn
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AUTHOR
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Clark Kimberling, Dec 26 2010
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STATUS
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approved
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