|
| |
|
|
A001650
|
|
n appears n times (n odd).
|
|
6
| |
|
|
1, 3, 3, 3, 5, 5, 5, 5, 5, 7, 7, 7, 7, 7, 7, 7, 9, 9, 9, 9, 9, 9, 9, 9, 9, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 15, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 1,2
|
|
|
COMMENTS
| For n >= 0, a(n+1) is the number of integers x with |x| <= sqrt(n), or equivalently the number of point in the Z^1 lattice of norm <= n+1. - David W. Wilson, Oct 22 2006
|
|
|
REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 106.
|
|
|
FORMULA
| a(n) = 1 + 2*floor(sqrt(n-1)), n > 0. - Antonio Esposito (antonio.b.esposito(AT)italtel.it), Jan 21 2002
G.f.: theta_3(x)*x/(1-x). a(n+1)=a(n)+A000122(n). - Michael Somos, Apr 29 2003.
a(1)=1,a(2)=3,a(3)=3,a(n)=a(n-a(n-2))+2 [From Branko Curgus (curgus(AT)wwu.edu), May 07 2010]
a(n)=2*ceiling(sqrt(n))-1 [From Branko Curgus (curgus(AT)wwu.edu), May 07 2010]
|
|
|
MATHEMATICA
| a[1]=1, a[2]=3, a[3]=3, a[n_]:=a[n]=a[n-a[n-2]]+2 [From Branko Curgus (curgus(AT)wwu.edu), May 07 2010]
|
|
|
PROG
| (PARI) a(n)=if(n<1, 0, 1+2*sqrtint(n-1))
|
|
|
CROSSREFS
| Cf. A001670. Partial sums of A000122.
Sequence in context: A136800 A126661 A162226 * A130175 A200266 A101290
Adjacent sequences: A001647 A001648 A001649 * A001651 A001652 A001653
|
|
|
KEYWORD
| nonn,easy
|
|
|
AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
|
|
|
EXTENSIONS
| More terms from Michael Somos, Apr 29 2003.
|
| |
|
|
