A027620 a(n) = n + (n+1)^2 + (n+2)^3.

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

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

Patrick De Geest, Palindromic Quasi_Under_Squares of the form n+(n+1)^2

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

Milan Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550 [math.CO], 2013.

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

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

(Sage) [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

Cf. A000027, A027621, A027622, A028387.

Sequence in context: A120498 A155098 A063134 * A152619 A051662 A326247

Adjacent sequences: A027617 A027618 A027619 * A027621 A027622 A027623

Keyword

nonn,easy

Author

Patrick De Geest

Status

approved