A000076 Number of integers <= 2^n of form 4 x^2 + 4 x y + 5 y^2.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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

Examples

			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.
		

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.
• Index entries for sequences related to populations of quadratic forms

Programs

PARI

a(n)=if(n<0,0,sum(k=1,2^n,0
				

Extensions

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