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A027620 a(n) = n + (n+1)^2 + (n+2)^3. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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

Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets

M. 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)/(x - 1)^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

MAPLE

[seq((n+3)^2*(n+1), n=0..40)]; # Zerinvary Lajos, Sep 24 2006

PROG

(Sage) [i+(i+1)^2+(i+2)^3 for i in xrange(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

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

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Last modified October 14 12:02 EDT 2019. Contains 328004 sequences. (Running on oeis4.)