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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, 10818037, 21208747, 41612533, 81704494, 160531078, 315602635, 620831732, 1221915127, 2406177404, 4740454046, 9343415302, 18423548106, 36342329321 (list; graph; refs; listen; history; text; internal format)
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
D. Shanks and L. P. Schmid, Variations on a theorem of Landau. Part I, Math. Comp., 20 (1966), 551-569.
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
KEYWORD
nonn
AUTHOR
EXTENSIONS
a(27)-a(39) from Bert Dobbelaere, Sep 24 2020
STATUS
approved

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Last modified March 29 09:59 EDT 2024. Contains 371268 sequences. (Running on oeis4.)