A000076 - OEIS

A000076

Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2.
(Formerly M1079 N0409)

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, 10818037, 21208747, 41612533, 81704494, 160531078, 315602635, 620831732, 1221915127, 2406177404, 4740454046, 9343415302, 18423548106, 36342329321

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OFFSET

0,4

COMMENTS

Rewriting the expression as (2 x + y)^2 + 4 y^2 facilitates an efficient search without negative terms. - Bert Dobbelaere, Sep 24 2020

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

Table of n, a(n) for n=0..39.

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

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: A048248 A370636 A056180 * A217730 A360055 A347760

Adjacent sequences: A000073 A000074 A000075 * A000077 A000078 A000079

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

a(27)-a(39) from Bert Dobbelaere, Sep 24 2020

STATUS

approved