

A001650


k appears k times (k odd).


18



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
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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 points in the Z^1 lattice of norm <= n+1.  David W. Wilson, Oct 22 2006
The burning number of a connected graph of order n is at most a(n). See Bessy et al.  Michel Marcus, Jun 18 2018


REFERENCES

J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", SpringerVerlag, p. 106.


LINKS

Stéphane Bessy, Anthony Bonato, Jeannette Janssen and Dieter Rautenbach, Bounds on the Burning Number, arXiv:1511.06023 [math.CO], 20152016.


FORMULA

G.f.: theta_3(x)*x/(1x).
a(1) = 1, a(2) = 3, a(3) = 3, a(n) = a(na(n2))+2.  Branko Curgus, May 07 2010
Seen as a triangle read by rows: T(n,k) = 2*(n1), k=1..n.  Reinhard Zumkeller, Nov 14 2015


MATHEMATICA

a[1]=1, a[2]=3, a[3]=3, a[n_]:=a[n]=a[na[n2]]+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(n1))
(Haskell)
a001650 n k = a001650_tabf !! (n1) !! (k1)
a001650_row n = a001650_tabf !! (n1)
a001650_tabf = iterate (\xs@(x:_) > map (+ 2) (x:x:xs)) [1]
a001650_list = concat a001650_tabf


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



EXTENSIONS



STATUS

approved



