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a(n) = n^6 - n^3.
1

%I #26 Sep 08 2022 08:45:32

%S 0,0,56,702,4032,15500,46440,117306,261632,530712,999000,1770230,

%T 2984256,4824612,7526792,11387250,16773120,24132656,34006392,47039022,

%U 63992000,85756860,113369256,148023722,191089152,244125000,308898200,387400806,481868352,594798932

%N a(n) = n^6 - n^3.

%H Vincenzo Librandi, <a href="/A136006/b136006.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (2*x^6 + 58*x^5 + 294*x^4 + 310*x^3 + 56*x^2)/(-x^7 + 7*x^6 - 21*x^5 + 35*x^4 - 35*x^3 + 21*x^2 - 7*x + 1). - _Alexander R. Povolotsky_, Apr 01 2008

%F a(n) = A001014(n) - A000578(n). - _Michel Marcus_, Feb 15 2014

%F a(n) = 2 * A085744(n). - _Alois P. Heinz_, Mar 15 2021

%p A136006:=n->n^6 - n^3; seq(A136006(n), n=0..60); # _Wesley Ivan Hurt_, Feb 14 2014

%t a[n_]:=n^6-n^3; a[Range[0,60]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2011 *)

%t CoefficientList[Series[(2 x^6 + 58 x^5 + 294 x^4 + 310 x^3 + 56 x^2)/(-x^7 + 7 x^6 - 21 x^5 + 35 x^4 - 35 x^3 + 21 x^2 - 7 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 16 2014 *)

%o (Magma) [n^6 - n^3: n in [0..40]]; // _Vincenzo Librandi_, Feb 16 2014

%o (PARI) a(n) = n^6 - n^3; \\ _Joerg Arndt_, Feb 16 2014

%Y Cf. A085744.

%K easy,nonn

%O 0,3

%A _Rolf Pleisch_, Mar 16 2008

%E Extended by _Ray Chandler_, Dec 13 2008