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URL: https://oeis.org/A027620

⇱ A027620 - OEIS

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A027620
a(n) = n + (n+1)^2 + (n+2)^3.
9
9, 32, 75, 144, 245, 384, 567, 800, 1089, 1440, 1859, 2352, 2925, 3584, 4335, 5184, 6137, 7200, 8379, 9680, 11109, 12672, 14375, 16224, 18225, 20384, 22707, 25200, 27869, 30720, 33759, 36992, 40425, 44064, 47915, 51984, 56277, 60800
OFFSET
0,1
COMMENTS
Numbers n > 0 such that x^3 + 2*x^2 + n factors over the integers. - James R. Buddenhagen, Apr 19 2005
LINKS
FORMULA
a(n) = (n+1)*(n+3)^2. - Zerinvary Lajos, Sep 24 2006, corrected Dec 21 2010
G.f.: (9 - 4*x + x^2)/(1 - x)^4. - R. J. Mathar, Dec 21 2010
a(n) = coefficient of x^3 in the Maclaurin expansion of -1/((n+3)*x^2 + (n+3)*x + 1). - Francesco Daddi, Aug 04 2011
E.g.f.: (9 + 23*x + 10*x^2 + x^3)*exp(x). - G. C. Greubel, Aug 05 2022
MAPLE
[seq((n+3)^2*(n+1), n=0..40)]; # Zerinvary Lajos, Sep 24 2006
MATHEMATICA
Table[n +(n+1)^2 +(n+2)^3, {n, 0, 40}] (* or *) LinearRecurrence[{4, -6, 4, -1}, {9, 32, 75, 144}, 40] (* Harvey P. Dale, Feb 23 2021 *)
PROG
(SageMath) [i+(i+1)^2+(i+2)^3 for i in range(0, 38)] # Zerinvary Lajos, Jul 03 2008
(Magma) [n + (n+1)^2 + (n+2)^3: n in [0..40]]; // Vincenzo Librandi, Aug 05 2011
(Maxima) A027620(n):=n + (n+1)^2 + (n+2)^3$ makelist(A027620(n), n, 0, 15); /* Martin Ettl, Dec 13 2012 */
(PARI) a(n)=n+(n+1)^2+(n+2)^3 \\ Charles R Greathouse IV, Oct 07 2015
CROSSREFS
KEYWORD
nonn,easy
STATUS
approved