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A000018 Number of positive integers <= 2^n of form x^2 + 16y^2.
(Formerly M0331 N0126)
0
1, 1, 2, 2, 4, 8, 13, 25, 44, 83, 152, 286, 538, 1020, 1942, 3725, 7145, 13781, 26627, 51572, 100099, 194633, 379037, 739250, 1443573, 2822186, 5522889, 10818417, 21209278, 41613288, 81705516, 160532194, 315604479, 620834222, 1221918604, 2406183020, 4740461247 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.

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

Table of n, a(n) for n=0..36.

Index entries for sequences related to populations of quadratic forms

PROG

(PARI) a(n)=local(A); if(n<0, 0, A=qfrep([1, 0; 0, 16], 2^n); sum(k=1, 2^n, A[k]!=0))

CROSSREFS

Sequence in context: A039941 A036761 A042979 * A075126 A098788 A190820

Adjacent sequences:  A000015 A000016 A000017 * A000019 A000020 A000021

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from David W. Wilson, Feb 07 2000

Definition corrected by Sean A. Irvine, Sep 09 2009

STATUS

approved

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Last modified March 28 22:27 EDT 2017. Contains 284249 sequences.