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A000050 Number of positive integers <= 2^n of form x^2 + y^2.
(Formerly M0715 N0265)
7
1, 2, 3, 5, 9, 16, 29, 54, 97, 180, 337, 633, 1197, 2280, 4357, 8363, 16096, 31064, 60108, 116555, 226419, 440616, 858696, 1675603, 3273643, 6402706, 12534812, 24561934, 48168461, 94534626, 185661958, 364869032, 717484560, 1411667114, 2778945873, 5473203125 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
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..50 (terms 0..35 from N. J. A. Sloane)
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.
Seth A. Troisi, C++ program
EXAMPLE
There are 5 integers <= 2^3 of the form x^2 + y^2. The five (x,y) pairs (x <= y) are (0,1), (1,1), (0,2), (1,2), (2,2) and give the integers 1, 2, 4, 5, 8, respectively. So a(3) = 5. - Seth A. Troisi, Apr 27 2022
MATHEMATICA
(* This program is not suitable for a large number of terms *) a[0] = 1; a[n_] := a[n] = (For[cnt = 0; k = 2^(n-1)+1, k <= 2^n, k++, If[SquaresR[2, k] > 0, cnt++]]; cnt + a[n-1]); Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 26}] (* Jean-François Alcover, Mar 20 2014 *)
PROG
(Haskell)
isqrt = a000196
issquare = a010052
a000050 n = foldl f 0 [1..2^n]
where f i j = if a000050' j > 0 then i + 1 else i
a000050' k = foldl f 0 (h k)
where f i y = g y + i
where g y = issquare (k - y^2)
h k = [0..isqrt k]
-- James Spahlinger, Oct 09 2012
CROSSREFS
Cf. A001481.
Sequence in context: A255071 A103285 A000049 * A050253 A198518 A182558
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified March 29 09:32 EDT 2024. Contains 371268 sequences. (Running on oeis4.)