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 A027620 n + (n+1)^2 + (n+2)^3. 4
 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 Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets M. Janjic and B. Petkovic, A Counting Function, arXiv 1301.4550, 2013 Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1) FORMULA a(n) = (n+1)*(n+3)^2. - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 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 (zerinvarylajos(AT)yahoo.com), Sep 24 2006 a:=n->sum(sum(binomial(n+1, n), j=2..n), k=0..n): seq(a(n), n=2..40); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 08 2007 MATHEMATICA f[n_]:=n^1+(n+1)^2+(n+2)^3; lst={}; Do[AppendTo[lst, f[n]], {n, 0, 5!}]; lst [From Vladimir Joseph Stephan Orlovsky, Jun 24 2009] PROG sage: [i+(i+1)^2+(i+2)^3 for i in xrange(0, 38)] - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jul 03 2008 (Sage) [lucas_number1(4, n, n) for n in xrange(3, 41)] # [Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 16 2009] (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 */ CROSSREFS Sequence in context: A120498 A155098 A063134 * A152619 A051662 A196016 Adjacent sequences:  A027617 A027618 A027619 * A027621 A027622 A027623 KEYWORD nonn,easy AUTHOR STATUS approved

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