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A000378
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Numbers of the form x^2 + y^2 + z^2 (x, y, z >= 0).
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28
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0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 24, 25, 26, 27, 29, 30, 32, 33, 34, 35, 36, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 54, 56, 57, 58, 59, 61, 62, 64, 65, 66, 67, 68, 69, 70, 72, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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REFERENCES
| J. H. Conway and N. J. A. Sloane, "Sphere Packings, Lattices and Groups", Springer-Verlag, p. 107.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 311.
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..10000
J. W. Cogdell, On sums of three squares
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 91. [?Broken link]
P. Pollack, Analytic and Combinatorial Number Theory Course Notes, p. 91.
Index entries for sequences related to sums of squares
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FORMULA
| Legendre: a nonnegative integer is a sum of three squares iff it is not of the form 4^k m with m == 7 (mod 8).
n^(2k+1) is in the sequence iff n is in the sequence. [From Ray Chandler (rayjchandler(AT)sbcglobal.net), Feb 03 2009]
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MATHEMATICA
| Take[Union[Flatten[Table[a^2+b^2+c^2, {a, 0, 16}, {b, 0, 16}, {c, 0, 16}]]], 234] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Feb 16 2010]
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PROG
| (PARI) isA000378(n)=my(k=valuation(n, 2)); if(k%2==0, n>>=k; n%8!=7, 1)
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CROSSREFS
| Union of {0}, A000290, A000404 and A000408.
Cf. A005875 (number of representations).
Cf. A004215, A047449, A034043-A034047, A065883, A072400, A072401, A071374.
Cf. A002828, A001481, A125084.
Sequence in context: A004777 A059561 A037474 * A022551 A172251 A187396
Adjacent sequences: A000375 A000376 A000377 * A000379 A000380 A000381
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Ray Chandler (rayjchandler(AT)sbcglobal.net), Sep 05 2004
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