OFFSET
0,5
REFERENCES
B. Alspach, K. Heinrich and G. Liu, Orthogonal factorizations of graphs, pp. 13-40 of Contemporary Design Theory, ed. J. H. Dinizt and D. R. Stinson, Wiley, 1992 (see Theorem 2.7).
LINKS
Robert Israel, Table of n, a(n) for n = 0..10000
FORMULA
From Robert Israel, Jun 13 2018: (Start)
a(n) = n-k for k^2-k+1 <= n <= k^2+k, k >= 1.
G.f.: x/(1-x)^2 - Theta_2(0,x)*x^(3/4)/(2*(1-x)) where Theta_2 is a Jacobi theta function. (End)
a(n) = n - floor(sqrt(n) + 1/2) = n - A000194(n). - Ridouane Oudra, May 13 2019
MAPLE
0, seq(seq(n-k, n=k^2-k+1..k^2+k), k=1..10); # Robert Israel, Jun 13 2018
MATHEMATICA
Table[Round[n-Sqrt[n]], {n, 0, 70}] (* Harvey P. Dale, Jun 15 2014 *)
PROG
(Magma) [n-Floor(Sqrt(n)+1/2):n in [0..80]]; // Marius A. Burtea, May 13 2019
(PARI) a(n) = round(n - sqrt(n)); \\ Michel Marcus, May 13 2019
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 07 2000
STATUS
approved