OFFSET
0,2
COMMENTS
Every term is the product plus the sum of 3 consecutive numbers. - Vladimir Joseph Stephan Orlovsky, Oct 24 2009
Continued fraction [n,n,n] = (n^2+1)/(n^3+2n) = (n^2+1)/a(n); e.g., [7,7,7] = 50/357. - Gary W. Adamson, Jul 15 2010
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..10000
Thomas Oléron Evans, Queues of Cubes, Mathistopheles, August 22 2015.
Aleksandar Petojević, A Note about the Pochhammer Symbol, Mathematica Moravica, Vol. 12-1 (2008), 37-42.
Michelle Rudolph-Lilith, On the Product Representation of Number Sequences, with Application to the Fibonacci Family, arXiv preprint arXiv:1508.07894 [math.NT], 2015.
Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
FORMULA
a(n) = n^3 + 2n = A073133(n, 3). - Henry Bottomley, Jul 16 2002
G.f.: 3*x*(x^2+1)/(x-1)^4. - Colin Barker, Dec 21 2012
a(n) = ((n-1)^3 + n^3 + (n+1)^3) / 3. - David Morales Marciel, Aug 28 2015
From Bernard Schott, Nov 28 2021: (Start)
a(n) = 3*A006527(n). (End)
MATHEMATICA
nterms=100; Table[n^3+2n, {n, 0, nterms}] (* Paolo Xausa, Nov 25 2021 *)
PROG
(PARI) a(n)=n^3+2*n \\ Charles R Greathouse IV, Sep 01 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 16 2000
STATUS
approved