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A033431 a(n) = 2*n^3. 16
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 (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

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

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

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

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

Cf. A000578, A002378, A033581, A117642, A213821.

Sequence in context: A027273 A210710 A225051 * A107610 A091914 A123791

Adjacent sequences:  A033428 A033429 A033430 * A033432 A033433 A033434

KEYWORD

nonn,easy

AUTHOR

Jeff Burch

STATUS

approved

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Last modified February 17 14:12 EST 2018. Contains 299296 sequences. (Running on oeis4.)