OFFSET
0,3
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).
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)
EXAMPLE
a(3) = T(3^3) - 3^3 = T(27) - 27 = 378 - 27 = 351.
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 *)
PROG
(PARI) t(n)=n*(n+1)/2; for(n=0, 30, print1(t(n^3)-n^3", "))
(Magma) [n^3*(n^3-1)/2: n in [0..40]]; // Vincenzo Librandi, Sep 14 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Jon Perry, Jul 21 2003
STATUS
approved