The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A038589 Sizes of successive clusters in hexagonal lattice A_2 centered at lattice point. 4
 1, 7, 7, 13, 19, 19, 19, 31, 31, 37, 37, 37, 43, 55, 55, 55, 61, 61, 61, 73, 73, 85, 85, 85, 85, 91, 91, 97, 109, 109, 109, 121, 121, 121, 121, 121, 127, 139, 139, 151, 151, 151, 151, 163, 163, 163, 163, 163, 169, 187, 187, 187, 199, 199, 199 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The hexagonal lattice is the familiar 2-dimensional lattice in which each point has 6 neighbors. This is sometimes called the triangular lattice. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..300 B. Cloitre, On the circle and divisor problems G. Nebe and N. J. A. Sloane, Home page for hexagonal (or triangular) lattice A2 FORMULA Partial sums of A004016. Expansion of a(x) / (1 - x) in powers of x where a() is a cubic AGM theta function (cf. A004016). - Michael Somos, Aug 21 2012 Equals 1 + A014201(n). - Neven Juric, May 10 2010 a(n) = 1 + 6*Sum_{k=1..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)) as for the Gauss circle or Dirichlet divisor problems. - Benoit Cloitre, Oct 27 2012 EXAMPLE 1 + 7*x + 7*x^2 + 13*x^3 + 19*x^4 + 19*x^5 + 19*x^6 + 31*x^7 + 31*x^8 + 37*x^9 + ... MATHEMATICA a[n_] := 1 + Sum[ Length[ {ToRules[ Reduce[ x^2 + x*y + y^2 == k, {x, y}, Integers] ]}], {k, 1, n}]; Table[a[n], {n, 0, 54}] (* Jean-François Alcover, Feb 23 2012, after Neven Juric *) PROG (PARI) a(n)=1+6*sum(k=0, n\3, (n\(3*k+1))-(n\(3*k+2))) CROSSREFS Cf. A004016, A014201, A038589, A038590. Sequence in context: A168301 A335895 A072821 * A332304 A317790 A109539 Adjacent sequences: A038586 A038587 A038588 * A038590 A038591 A038592 KEYWORD nonn,easy,nice AUTHOR STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified March 25 09:47 EDT 2023. Contains 361520 sequences. (Running on oeis4.)