A000018 Number of positive integers <= 2^n of form x^2 + 16*y^2. (Formerly M0331 N0126)

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

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

Delbert L. Johnson, Table of n, a(n) for n = 0..45

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

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 * A357307 A306604 A389508

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