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

0,3

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

Cf. A000217.

Sequence in context: A022720 A272174 A173421 * A163719 A138452 A276286

Adjacent sequences: A085741 A085742 A085743 * A085745 A085746 A085747

Keyword

nonn,easy

Author

Jon Perry, Jul 21 2003

Status

approved