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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
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), 551-569.
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 * A383253 A000050 A050253
KEYWORD
nonn
STATUS
approved