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A005752
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a(n) = n^2 + n*floor(n*tau) - floor(n*tau)^2.
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1
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0, 1, 1, 5, 4, 1, 9, 5, 16, 11, 4, 19, 11, 1, 20, 9, 31, 19, 5, 31, 16, 45, 29, 11, 44, 25, 4, 41, 19, 59, 36, 11, 55, 29, 1, 49, 20, 71, 41, 9, 64, 31, 89, 55, 19, 81, 44, 5, 71, 31, 100, 59, 16, 89, 45, 121, 76, 29, 109
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OFFSET
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0,4
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LINKS
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Table of n, a(n) for n=0..58.
P. Fahr, Infinite Gabriel-Roiter measures for the 3-Kronecker quiver, PhD Thesis U. Bielefeld (2008) p 45
Clark Kimberling, The equation m^2 - 4k = 5n^2 and unique representations of positive integers, Fibonacci Quart. 45 (2007), no. 4, 304-312.
Rodica Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1981), 97.
Rodica Simion, Trees with 1-factors and oriented trees, Discrete Math., 88 (1981), 97. (Annotated scanned copy)
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MATHEMATICA
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Table[n^2 + n Floor[n #] - Floor[n #]^2 &@ GoldenRatio, {n, 0, 60}] (* Michael De Vlieger, Mar 06 2016 *)
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PROG
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(PARI) a(n) = my(fnt = floor(n*(sqrt(5)+1)/2)); n^2 + n*fnt - fnt^2; \\ Michel Marcus, Mar 05 2016
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CROSSREFS
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Sequence in context: A197001 A308714 A213055 * A098494 A008955 A182824
Adjacent sequences: A005749 A005750 A005751 * A005753 A005754 A005755
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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