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a(n) = A000217(n^3) - n^3.
4

%I #25 Sep 08 2022 08:45:11

%S 0,0,28,351,2016,7750,23220,58653,130816,265356,499500,885115,1492128,

%T 2412306,3763396,5693625,8386560,12066328,17003196,23519511,31996000,

%U 42878430,56684628,74011861,95544576,122062500,154449100,193700403,240934176,297399466,364486500

%N a(n) = A000217(n^3) - n^3.

%H Vincenzo Librandi, <a href="/A085744/b085744.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F a(n) = n^3*(n^3 - 1)/2. - _Vincenzo Librandi_, Sep 14 2011

%F From _Chai Wah Wu_, Aug 08 2022: (Start)

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n > 6.

%F G.f.: -x^2*(x^4 + 29*x^3 + 147*x^2 + 155*x + 28)/(x - 1)^7. (End)

%e a(3) = T(3^3) - 3^3 = T(27) - 27 = 378 - 27 = 351.

%t Table[(n^6-n^3)/2,{n,0,60}] (* _Vladimir Joseph Stephan Orlovsky_, Feb 28 2011 *)

%t (#(#-1))/2&/@(Range[0,30]^3) (* _Harvey P. Dale_, Dec 26 2021 *)

%o (PARI) t(n)=n*(n+1)/2; for(n=0,30,print1(t(n^3)-n^3","))

%o (Magma) [n^3*(n^3-1)/2: n in [0..40]]; // _Vincenzo Librandi_, Sep 14 2011

%Y Cf. A000217.

%K nonn,easy

%O 0,3

%A _Jon Perry_, Jul 21 2003