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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 (list; graph; refs; listen; history; text; internal format)
 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 * A000050 A050253 A198518 Adjacent sequences: A000046 A000047 A000048 * A000050 A000051 A000052 KEYWORD nonn AUTHOR STATUS approved

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Last modified December 9 23:05 EST 2022. Contains 358710 sequences. (Running on oeis4.)