A132998 a(n) = n^4 - n^3 - n^2.
0, -1, 4, 45, 176, 475, 1044, 2009, 3520, 5751, 8900, 13189, 18864, 26195, 35476, 47025, 61184, 78319, 98820, 123101, 151600, 184779, 223124, 267145, 317376, 374375, 438724, 511029, 591920, 682051, 782100, 892769
Offset: 0
Examples
a(7)=2009 because 7^4=2401, 7^3=343, 7^2=49 and we can write 2401-343-49=2009.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Magma
[n^4-n^3-n^2: n in [0..50]]; // Vincenzo Librandi, Dec 15 2010
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Maple
A132998:=n->n^4-n^3-n^2; seq(A132998(n), n=0..50); # Wesley Ivan Hurt, May 21 2014
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Mathematica
f[n_]:=n^4-n^3-n^2; Table[f[n],{n,5!}] (* Vladimir Joseph Stephan Orlovsky, Dec 04 2009 *) CoefficientList[Series[- x (-1 + 9 x + 15 x^2 + x^3)/(-1 + x)^5, {x, 0, 50}], x] (* Vincenzo Librandi, May 21 2014 *) LinearRecurrence[{5,-10,10,-5,1}, {0, -1, 4, 45, 176}, 50] (* G. C. Greubel, Sep 28 2017 *) -
PARI
x='x+O('x^50); Vec(x*(-1+9*x+15*x^2+x^3)/(1-x)^5) \\ G. C. Greubel, Sep 28 2017
Formula
a(n) = n^4 - n^3 - n^2.
G.f.: x*(-1+9*x+15*x^2+x^3)/(1-x)^5. - R. J. Mathar, Nov 14 2007