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A001650 n appears n times (n odd). 18

%I

%S 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,

%T 11,11,11,11,11,13,13,13,13,13,13,13,13,13,13,13,13,13,15,15,15,15,15,

%U 15,15,15,15,15,15,15,15,15,15,17,17,17,17,17,17,17,17,17,17,17,17,17

%N n appears n times (n odd).

%C 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

%C The burning number of a connected graph of order n is at most a(n). See Bessy et al. - _Michel Marcus_, Jun 18 2018

%D J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 106.

%H T. D. Noe, <a href="/A001650/b001650.txt">Table of n, a(n) for n = 1..10000</a>

%H St├ęphane Bessy, Anthony Bonato, Jeannette Janssen and Dieter Rautenbach, <a href="https://arxiv.org/abs/1511.06023">Bounds on the Burning Number</a>, arXiv:1511.06023 [math.CO], 2015-2016.

%H Abraham Isgur, Vitaly Kuznetsov, and Stephen Tanny, <a href="https://arxiv.org/abs/1202.0276">A combinatorial approach for solving certain nested recursions with non-slow solutions</a>, arXiv preprint arXiv:1202.0276 [math.CO], 2012.

%F a(n) = 1 + 2*floor(sqrt(n-1)), n > 0. - Antonio Esposito (antonio.b.esposito(AT)italtel.it), Jan 21 2002

%F G.f.: theta_3(x)*x/(1-x). a(n+1)=a(n)+A000122(n). - _Michael Somos_, Apr 29 2003.

%F a(1) = 1, a(2) = 3, a(3) = 3, a(n) = a(n-a(n-2))+2. - _Branko Curgus_, May 07 2010

%F a(n) = 2*ceiling(sqrt(n))-1. - _Branko Curgus_, May 07 2010

%F Seen as a triangle read by rows: T(n,k) = 2*(n-1), k=1..n. - _Reinhard Zumkeller_, Nov 14 2015

%t a[1]=1,a[2]=3,a[3]=3,a[n_]:=a[n]=a[n-a[n-2]]+2 (* _Branko Curgus_, May 07 2010 *)

%t Flatten[Table[Table[n,{n}],{n,1,17,2}]] (* _Harvey P. Dale_, Mar 31 2013 *)

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

%o (Haskell)

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

%o a001650_row n = a001650_tabf !! (n-1)

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

%o a001650_list = concat a001650_tabf

%o -- _Reinhard Zumkeller_, Nov 14 2015

%Y Cf. A001670. Partial sums of A000122.

%Y Cf. A111650, A131507, A193832.

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_.

%E More terms from _Michael Somos_, Apr 29 2003

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Last modified April 11 22:01 EDT 2021. Contains 342888 sequences. (Running on oeis4.)