A005752 a(n) = n^2 + n*floor(n*tau) - floor(n*tau)^2.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Links

• 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)

Programs

Mathematica

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

PARI

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