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A027620
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n + (n+1)^2 + (n+2)^3.
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4
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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;
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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COMMENTS
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Numbers n>0 such that x^3 + 2*x^2 + n factors over the integers. - James R. Buddenhagen, Apr 19 2005
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LINKS
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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, 2013
Index to sequences with linear recurrences with constant coefficients, signature (4,-6,4,-1)
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FORMULA
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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]
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MAPLE
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[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
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MATHEMATICA
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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]
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PROG
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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 */
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CROSSREFS
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Sequence in context: A120498 A155098 A063134 * A152619 A051662 A196016
Adjacent sequences: A027617 A027618 A027619 * A027621 A027622 A027623
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KEYWORD
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nonn,easy
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AUTHOR
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Patrick De Geest
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STATUS
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approved
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