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A014201 Number of solutions to x^2+x*y+y^2 <= n excluding (0,0). 3
0, 6, 6, 12, 18, 18, 18, 30, 30, 36, 36, 36, 42, 54, 54, 54, 60, 60, 60, 72, 72, 84, 84, 84, 84, 90, 90, 96, 108, 108, 108, 120, 120, 120, 120, 120, 126, 138, 138, 150, 150, 150, 150, 162, 162, 162, 162, 162, 168 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..300

B. Cloitre, On the circle and divisor problems

FORMULA

Equals A038589(n) - 1. - Neven Juric, May 10 2010

a(n) = 6*sum(k=0,n/3,floor(n/(3k+1))-floor(n/(3k+2))). a(n) is asymptotic to 2*Pi/sqrt(3)*n. Conjecture: a(n)=2*Pi/sqrt(3)*n+O(n^(1/4+epsilon)) like for the Gauss circle or Dirichlet divisor problems - Benoit Cloitre, Oct 27 2012

MATHEMATICA

a[n_] := Sum[ Length[ {ToRules[ Reduce[ x^2 + x*y + y^2 == k, {x, y}, Integers]]}], {k, 1, n}]; Table[ a[n], {n, 0, 48}] (* Jean-Fran├žois Alcover, Feb 23 2012 *)

PROG

(PARI) a(n)=6*sum(k=0, n\3, (n\(3*k+1))-(n\(3*k+2))) \\ Benoit Cloitre, Oct 27 2012

CROSSREFS

Cf. A014202, A014198.

Sequence in context: A046625 A315787 A029682 * A315788 A315789 A315790

Adjacent sequences:  A014198 A014199 A014200 * A014202 A014203 A014204

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 19 11:10 EDT 2019. Contains 321329 sequences. (Running on oeis4.)