A054602 a(n) = Sum_{d|3} phi(d)*n^(3/d).
0, 3, 12, 33, 72, 135, 228, 357, 528, 747, 1020, 1353, 1752, 2223, 2772, 3405, 4128, 4947, 5868, 6897, 8040, 9303, 10692, 12213, 13872, 15675, 17628, 19737, 22008, 24447, 27060, 29853, 32832, 36003, 39372, 42945, 46728, 50727, 54948, 59397, 64080, 69003, 74172
Offset: 0
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), pp. 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).
Programs
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Mathematica
nterms=100;Table[n^3+2n,{n,0,nterms}] (* Paolo Xausa, Nov 25 2021 *) -
PARI
a(n)=n^3+2*n \\ Charles R Greathouse IV, Sep 01 2015
Formula
a(n) = n^3 + 2*n = 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)
From Elmo R. Oliveira, Aug 09 2025: (Start)
E.g.f.: exp(x)*x*(3 + 3*x + x^2).
a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4).
a(n) = A292022(n)/4. (End)
Comments