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A033431 a(n) = 2*n^3. 24
0, 2, 16, 54, 128, 250, 432, 686, 1024, 1458, 2000, 2662, 3456, 4394, 5488, 6750, 8192, 9826, 11664, 13718, 16000, 18522, 21296, 24334, 27648, 31250, 35152, 39366, 43904, 48778, 54000, 59582, 65536, 71874, 78608, 85750, 93312, 101306, 109744, 118638, 128000, 137842 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
Also the largest determinant of a 3 X 3 matrix with entries from {0..n}. - Jud McCranie, Aug 12 2001
4*a(n) is a perfect cube.
The positive terms comprise the principal diagonal of the convolution array A213821. - Clark Kimberling, Jul 04 2012
Volume of a pyramid (square base) with side n and height 6*n. - Wesley Ivan Hurt, Aug 25 2014
LINKS
Amelia Carolina Sparavigna, Generalized Sum of Stella Octangula Numbers, Politecnico di Torino (Italy, 2021).
Amelia Carolina Sparavigna, Cardano Formula and Some Figurate Numbers, Politecnico di Torino (Italy, 2021).
FORMULA
G.f.: 2*x*(1 + 4*x + x^2) / (1 - x)^4. - R. J. Mathar, Feb 04 2011
a(n) = 2*A000578(n). - Omar E. Pol, May 14 2008
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4). - Wesley Ivan Hurt, Aug 25 2014
a(n) = A002378(n)^2 - A002378(n^2). - Bruno Berselli, Oct 20 2016
E.g.f.: 2*x*(1 + 3*x + x^2)*exp(x). - G. C. Greubel, Jul 15 2017
From Amiram Eldar, Jan 10 2023: (Start)
Sum_{n>=1} 1/a(n) = zeta(3)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = 3*zeta(3)/8. (End)
MAPLE
seq(2*n^3, n=0..39); # Nathaniel Johnston, Jun 26 2011
MATHEMATICA
2 Range[0, 50]^3 (* Wesley Ivan Hurt, Aug 25 2014 *)
PROG
(Magma) [2*n^3: n in [0..30]]; // Vincenzo Librandi, Jun 26 2011
(PARI) a(n)=2*n^3 \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
Sequence in context: A210710 A337529 A225051 * A107610 A091914 A123791
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified March 19 01:22 EDT 2024. Contains 370952 sequences. (Running on oeis4.)