

A000049


Number of positive integers <= 2^n of the form 3*x^2 + 4*y^2.
(Formerly M0714 N0264)


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
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OFFSET

0,3


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), 551569.
Index entries for sequences related to populations of quadratic forms


EXAMPLE

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


CROSSREFS

Cf. A020677.
Sequence in context: A192804 A255071 A103285 * A000050 A050253 A198518
Adjacent sequences: A000046 A000047 A000048 * A000050 A000051 A000052


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



