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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 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

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Last modified September 13 20:16 EDT 2024. Contains 375910 sequences. (Running on oeis4.)