A016755 Odd cubes: a(n) = (2*n + 1)^3.

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

Offset

0,2

Comments

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

References

Steven R. Finch, Mathematical Constants, Encyclopedia of Mathematics and its Applications, vol. 94, Cambridge University Press, 2003, Section 1.6.3.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..10000

Marc Chamberland and Armin Straub, On gamma quotients and infinite products, Advances in Applied Mathematics, Vol. 51, No. 5 (2013), pp. 546-562.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

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

Product_{n>=1} (1 - (-1)^n/a(n)) = (Pi/12)*(1 + sqrt(2)*cosh(sqrt(3)*Pi/4)) (Chamberland and Straub, 2013). - Amiram Eldar, Jan 26 2024

Mathematica

Range[1, 101, 2]^3 (* Harvey P. Dale, Nov 18 2013 *)

Prog

(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

Crossrefs

Cf. A000578, A005408, A010014, A016743, A153071, A154537.

Cf. A000330, A005917, A069074.

Sequence in context: A118092 A371189 A126272 * A074100 A082610 A061434

Adjacent sequences: A016752 A016753 A016754 * A016756 A016757 A016758

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved