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

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A000205 Number of positive integers <= 2^n of form x^2 + 3 y^2. (Formerly M2350 N0928) 1
 1, 1, 3, 4, 8, 14, 25, 45, 82, 151, 282, 531, 1003, 1907, 3645, 6993, 13456, 25978, 50248, 97446, 189291, 368338, 717804, 1400699, 2736534, 5352182, 10478044, 20531668, 40264582, 79022464, 155196838, 304997408, 599752463, 1180027022, 2322950591, 4575114295 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 REFERENCES N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence). N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Seth A. Troisi, Table of n, a(n) for n = 0..45 P. Moree and H. J. J. te Riele, The hexagonal versus the square lattice, arXiv:math/0204332 [math.NT], 2002. P. Moree and H. J. J. te Riele, The hexagonal versus the square lattice, Math. Comp. 73 (2004), no. 245, 451-473. D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569. Index entries for sequences related to populations of quadratic forms MATHEMATICA (* This program is not suitable to compute more than a score of terms. *) a[0] = a[1] = 1; a[n_] := a[n] = Module[{cnt, k, r, x, y}, For[cnt = a[n-1]; k = 2^(n-1)+1, k <= 2^n, k++, r = Reduce[x >= 0 && y >= 0 && k == x^2 + 3 y^2, {x, y}, Integers]; If[r =!= False, cnt++]]; cnt]; Table[Print[n, " ", a[n]]; a[n], {n, 0, 20}] (* Jean-François Alcover, Jan 23 2019 *) CROSSREFS Cf. A000050, A003136. Sequence in context: A023623 A023558 A170902 * A136425 A331330 A005907 Adjacent sequences: A000202 A000203 A000204 * A000206 A000207 A000208 KEYWORD nonn AUTHOR N. J. A. Sloane 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 September 28 13:18 EDT 2023. Contains 365735 sequences. (Running on oeis4.)