A085744 a(n) = A000217(n^3) - n^3.
0, 0, 28, 351, 2016, 7750, 23220, 58653, 130816, 265356, 499500, 885115, 1492128, 2412306, 3763396, 5693625, 8386560, 12066328, 17003196, 23519511, 31996000, 42878430, 56684628, 74011861, 95544576, 122062500, 154449100, 193700403, 240934176, 297399466, 364486500
Offset: 0
Examples
a(3) = T(3^3) - 3^3 = T(27) - 27 = 378 - 27 = 351.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
-
Magma
[n^3*(n^3-1)/2: n in [0..40]]; // Vincenzo Librandi, Sep 14 2011
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Mathematica
Table[(n^6-n^3)/2,{n,0,60}] (* Vladimir Joseph Stephan Orlovsky, Feb 28 2011 *) (#(#-1))/2&/@(Range[0,30]^3) (* Harvey P. Dale, Dec 26 2021 *) -
PARI
t(n)=n*(n+1)/2; for(n=0,30,print1(t(n^3)-n^3","))
Formula
a(n) = n^3*(n^3 - 1)/2. - Vincenzo Librandi, Sep 14 2011
From Chai Wah Wu, Aug 08 2022: (Start)
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.
G.f.: -x^2*(x^4 + 29*x^3 + 147*x^2 + 155*x + 28)/(x - 1)^7. (End)