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A016755
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Odd cubes: a(n) = (2*n + 1)^3.
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23
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1, 27, 125, 343, 729, 1331, 2197, 3375, 4913, 6859, 9261, 12167, 15625, 19683, 24389, 29791, 35937, 42875, 50653, 59319, 68921, 79507, 91125, 103823, 117649, 132651, 148877, 166375, 185193, 205379, 226981, 250047, 274625, 300763, 328509, 357911, 389017, 421875
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OFFSET
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0,2
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COMMENTS
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Partial sums of A010014. - Jani Melik, May 20 2013
Terms end in the repeating sequence 1, 7, 5, 3, 9, ... - Melvin Peralta, Jul 08 2015
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REFERENCES
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S. R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, Section 1.6.3.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..10000
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
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FORMULA
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Sum_{n >= 0} 1/a(n) = 7 * zeta(3) / 8.
G.f.: (1+23*x+23*x^2+x^3)/(1-4*x+6*x^2-4*x^3+x^4). - Colin Barker, Jan 02 2012
a(n) = A000578(A005408(n)). - Michel Marcus, Jul 09 2015
E.g.f.: exp(x)*(1 + 26*x + 36*x^2 + 8*x^3). See A154537, row n=3. - Wolfdieter Lang, Mar 12 2017
From Bruce J. Nicholson, Dec 08 2019: (Start)
a(n) = 24 * A000330(n) + A005408(n).
a(n) = 2 * A005917(n+1) - A005408(n). (End)
Sum_{n>=0} (-1)^n/a(n) = Pi^3/32 (A153071). - Amiram Eldar, Oct 10 2020
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MATHEMATICA
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Range[1, 101, 2]^3 (* Harvey P. Dale, Nov 18 2013 *)
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PROG
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(MAGMA) [(2*n+1)^3: n in [0..50]]; // Vincenzo Librandi, Sep 05 2011
(PARI) a(n)=(2*n+1)^3 \\ Charles R Greathouse IV, Jan 02 2012
(Python)
def a(n): return (2*n+1)**3
print([a(n) for n in range(38)]) # Michael S. Branicky, Jan 27 2021
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CROSSREFS
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Cf. A000578, A005408, A010014, A016743, A153071, A154537.
Cf. A000330, A005917, A069074.
Sequence in context: A179145 A118092 A126272 * A074100 A082610 A061434
Adjacent sequences: A016752 A016753 A016754 * A016756 A016757 A016758
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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