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A005752 a(n) = n^2 + n*floor(n*tau) - floor(n*tau)^2. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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)

MATHEMATICA

Table[n^2 + n Floor[n #] - Floor[n #]^2 &@ GoldenRatio, {n, 0, 60}] (* Michael De Vlieger, Mar 06 2016 *)

PROG

(PARI) a(n) = my(fnt = floor(n*(sqrt(5)+1)/2));  n^2 + n*fnt - fnt^2; \\ Michel Marcus, Mar 05 2016

CROSSREFS

Sequence in context: A197001 A308714 A213055 * A098494 A008955 A182824

Adjacent sequences:  A005749 A005750 A005751 * A005753 A005754 A005755

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified June 5 12:47 EDT 2020. Contains 334840 sequences. (Running on oeis4.)