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A001650 n appears n times (n odd). 10
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; text; 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.

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

Abraham Isgur, Vitaly Kuznetsov, and Stephen Tanny, A combinatorial approach for solving certain nested recursions with non-slow solutions, arXiv preprint arXiv:1202.0276, 2012

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. - Branko Curgus, May 07 2010

a(n)=2*ceiling(sqrt(n))-1. - Branko Curgus, May 07 2010

Seen as a triangle read by rows: T(n,k) = 2*(n-1), k=1..n. - Reinhard Zumkeller, Nov 14 2015

MATHEMATICA

a[1]=1, a[2]=3, a[3]=3, a[n_]:=a[n]=a[n-a[n-2]]+2 (* Branko Curgus, May 07 2010 *)

Flatten[Table[Table[n, {n}], {n, 1, 17, 2}]] (* Harvey P. Dale, Mar 31 2013 *)

PROG

(PARI) a(n)=if(n<1, 0, 1+2*sqrtint(n-1))

(Haskell)

a001650 n k = a001650_tabf !! (n-1) !! (k-1)

a001650_row n = a001650_tabf !! (n-1)

a001650_tabf = iterate (\xs@(x:_) -> map (+ 2) (x:x:xs)) [1]

a001650_list = concat a001650_tabf

-- Reinhard Zumkeller, Nov 14 2015

CROSSREFS

Cf. A001670. Partial sums of A000122.

Cf. A111650, A131507, A193832.

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.

EXTENSIONS

More terms from Michael Somos, Apr 29 2003.

STATUS

approved

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Last modified March 27 06:40 EDT 2017. Contains 284144 sequences.