A000049 Number of positive integers <= 2^n of the form 3*x^2 + 4*y^2.

0, 0, 2, 3, 5, 9, 16, 29, 53, 98, 181, 341, 640, 1218, 2321, 4449, 8546, 16482, 31845, 61707, 119760, 232865, 453511, 884493, 1727125, 3376376, 6607207, 12941838, 25371086, 49776945, 97730393, 192009517, 377473965, 742511438, 1461351029, 2877568839, 5668961811

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

Examples

			There are 5 integers <= 2^4 of the form 3*x^2 + 4*y^2. The five (x,y) pairs are (1,0), (0,1), (1,1), (2,0), (0,2) and give 3, 4, 7, 12, 16 solutions, respectively. So a(4) = 5. - _Seth A. Troisi_, Apr 22 2022
		

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

• Seth A. Troisi, Table of n, a(n) for n = 0..49 (terms 0..36 from N. J. A. Sloane)
• Robert G. Donnelly, Molly W. Dunkum, Sasha V. Malone, and Alexandra Nance, Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras, arXiv:2012.14991 [math.CO], 2020.
• 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

Crossrefs

Cf. A020677.