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%I M0714 N0264 #40 May 13 2022 07:58:11
%S 0,0,2,3,5,9,16,29,53,98,181,341,640,1218,2321,4449,8546,16482,31845,
%T 61707,119760,232865,453511,884493,1727125,3376376,6607207,12941838,
%U 25371086,49776945,97730393,192009517,377473965,742511438,1461351029,2877568839,5668961811
%N Number of positive integers <= 2^n of the form 3*x^2 + 4*y^2.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Seth A. Troisi, <a href="/A000049/b000049.txt">Table of n, a(n) for n = 0..49</a> (terms 0..36 from N. J. A. Sloane)
%H Robert G. Donnelly, Molly W. Dunkum, Sasha V. Malone, and Alexandra Nance, <a href="https://arxiv.org/abs/2012.14991">Symmetric Fibonaccian distributive lattices and representations of the special linear Lie algebras</a>, arXiv:2012.14991 [math.CO], 2020.
%H D. Shanks and L. P. Schmid, <a href="http://dx.doi.org/10.1090/S0025-5718-1966-0210678-1">Variations on a theorem of Landau. Part I</a>, Math. Comp., 20 (1966), 551-569.
%H <a href="/index/Qua#quadpop">Index entries for sequences related to populations of quadratic forms</a>
%e 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
%Y Cf. A020677.
%K nonn
%O 0,3
%A _N. J. A. Sloane_
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