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A000592
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Number of nonnegative solutions of x^2 + y^2 = z in first n shells.
(Formerly M2324 N0919)
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1
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1, 3, 4, 6, 8, 9, 11, 13, 15, 17, 19, 20, 22, 26, 28, 30, 31, 33, 35, 37, 39, 41, 43, 45, 48, 50, 52, 54, 56, 58, 62, 64, 65, 67, 69, 71, 73, 75, 79, 81, 83, 85, 86, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 112, 113, 117, 119, 121, 123, 127, 129, 131, 133, 135, 137
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| N_2(t)= sum_{j <= t}n_2(j) where n_2(j) is the number of nonnegative solutions (x,y) of x^ 2+y^ 2=j, the solution (x,y) being considered as different from (y,x) in case x != y.
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REFERENCES
| Gupta, Hansraj; A table of values of N_2(t). Res. Bull. East Panjab Univ. 1952, (1952). no. 20, 13-93.
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).
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LINKS
| T. D. Noe, Table of n, a(n) for n=0..2749
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FORMULA
| Cumulative totals of nonzero values in (or distinct values in cumulative totals of) A000925. - Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 21 2006
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MATHEMATICA
| nn = 200; t = CoefficientList[Series[Sum[x^k^2, {k, 0, Sqrt[nn]}]^2, {x, 0, nn}], x]; Union[Accumulate[t]] (* From Jean-François Alcover, Jul 20 2011, after T. D. Noe *)
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CROSSREFS
| Cf. A000925.
Sequence in context: A133280 A138097 A193732 * A138924 A188015 A192284
Adjacent sequences: A000589 A000590 A000591 * A000593 A000594 A000595
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KEYWORD
| nonn,nice,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 21 2006
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