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A000076 Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2.
(Formerly M1079 N0409)
1
0, 0, 1, 2, 4, 7, 14, 24, 43, 82, 149, 284, 534, 1015, 1937, 3713, 7136, 13759, 26597, 51537, 100045, 194586, 378987, 739161, 1443465, 2821923, 5522689 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

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..26.

Index entries for sequences related to populations of quadratic forms

EXAMPLE

a(4)=4 since 2^4=16 and 4=4*1^2, 5=5*1^2, 13=4*1^2+4*1*1+5*1^2, 16=4*2^2.

PROG

(PARI) a(n)=if(n<0, 0, sum(k=1, 2^n, 0<sum(j=0, sqrtint(k)\2, issquare(k-4*j^2)&(k-j)%2==0)))

CROSSREFS

Sequence in context: A000075 A048248 A056180 * A217730 A218576 A054169

Adjacent sequences:  A000073 A000074 A000075 * A000077 A000078 A000079

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified March 26 23:19 EDT 2017. Contains 284141 sequences.