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A054602 a(n) = Sum_{d|3} phi(d)*n^(3/d). 11
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) = product plus 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

Table of n, a(n) for n=0..38.

Thomas Oléron Evans, Queues of Cubes, Mathistopheles, August 22 2015.

Michelle Rudolph-Lilith, On the Product Representation of Number Sequences, with Application to the Fibonacci Family, arXiv preprint arXiv:1508.07894, 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

MAPLE

with(combinat, fibonacci):seq(fibonacci(4, i), i=0..38); # Zerinvary Lajos, Dec 01 2006

MATHEMATICA

lst={}; Do[p=(n+2)*(n+1)*n+(n+2)+(n+1)+n; AppendTo[lst, p], {n, 0, 5!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 24 2009 *)

PROG

(Sage) [lucas_number1(4, n, -1) for n in xrange(0, 39)] # Zerinvary Lajos, May 16 2009

(PARI) a(n)=n^3+2*n \\ Charles R Greathouse IV, Sep 01 2015

CROSSREFS

Row n=3 of A185651.

Sequence in context: A288605 A268768 A174963 * A083725 A192972 A159228

Adjacent sequences:  A054599 A054600 A054601 * A054603 A054604 A054605

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Apr 16 2000

STATUS

approved

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Last modified February 24 03:21 EST 2018. Contains 299595 sequences. (Running on oeis4.)