A000413 - OEIS

A000413

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 A(A000092(n)).
(Formerly M4367 N1833)

1, 7, 19, 57, 81, 251, 437, 691, 739, 1743, 3695, 6619, 8217, 9771, 14771, 15155, 16831, 18805, 26745, 30551, 41755, 46297, 54339, 72359, 86407, 96969, 131059, 344859, 395231, 519963, 607141, 677397, 741509, 893019, 917217, 1288415, 1406811, 1789599, 1827927, 3085785, 3216051, 3444439, 3524869

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OFFSET

0,2

COMMENTS

The initial value a(0) = 1 corresponds to an initial A000092(0) = 0 which is the index of a record in the sense that the value P(0) = 0 is larger than all preceding values, because there are none. - M. F. Hasler, May 04 2022

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

Table of n, a(n) for n=0..42.

W. C. Mitchell, The number of lattice points in a k-dimensional hypersphere, Math. Comp., 20 (1966), 300-310.

FORMULA

a(n) = A117609(A000092(n)), considering A000092(0) = 0. - M. F. Hasler, May 04 2022

MATHEMATICA

P[n_] := (s = Sum[SquaresR[3, k], {k, 0, n}]) - Round[(4/3)*Pi*n^(3/2)]; record = 0; A000092 = Reap[For[n = 0, n <= 10^4, n++, If[(p = Abs[P[n]]) > record, record = p; Print[s]; Sow[s]]]][[2, 1]] (* Jean-François Alcover, Feb 08 2016, after M. F. Hasler in A000092 *)

CROSSREFS

Cf. A000323, A000036, A000092, A000099, A000223.

Cf. A117609 (A(n) in name).

Sequence in context: A002714 A126361 A069005 * A263335 A155335 A155226

Adjacent sequences: A000410 A000411 A000412 * A000414 A000415 A000416

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

EXTENSIONS

Revised Jun 28 2005

a(37)-a(42) from Vincenzo Librandi, Aug 21 2016

STATUS

approved

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