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A000223
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Let A(n) = #{(i,j,k): i^2 + j^2 + k^2 <= n}, V(n) = (4/3)Pi*n^(3/2), P(n) = A(n) - V(n); A000092 gives values of n where |P(n)| sets a new record; sequence gives (nearest integer to, I believe) P(A00092(n)).
(Formerly M2619 N1036)
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7
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3, 7, 10, 19, 32, 34, 37, 51, 81, 119, 122, 134, 157, 160, 161, 174, 221, 252, 254, 294, 305, 309, 364, 371, 405, 580, 682, 734, 756, 763, 776, 959, 1028, 1105, 1120, 1170, 1205, 1550, 1570, 1576, 1851, 1930, 2028, 2404, 2411, 2565, 2675, 2895, 2905, 2940, 3133
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OFFSET
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1,1
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COMMENTS
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Record values of (absolute values of) A210641 = A117609-A210639. It appears that the records occur always at positive elements of that sequence. (One could add an initial a(0)=1.) - M. F. Hasler, Mar 26 2012
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REFERENCES
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W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.
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
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Table of n, a(n) for n=1..51.
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FORMULA
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A000223(n) = |A210641(A000092(n))|. - M. F. Hasler, Mar 26 2012
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PROG
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(PARI) m=0; for(n=0, 1e4, m<abs(A210641(n)) & print1(m=A210641(n)", ")) /* This would print a negative value in case the record in absolute value occured for A117609(n)<A210639(n), which does not happen for n<10^4. */ - M. F. Hasler, Mar 26 2012
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CROSSREFS
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Cf. A000323, A000036, A000092, A000413, A000099.
Sequence in context: A024330 A069153 A167390 * A031328 A053159 A024464
Adjacent sequences: A000220 A000221 A000222 * A000224 A000225 A000226
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane.
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EXTENSIONS
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Revised Jun 28 2005
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STATUS
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approved
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