A101374 a(n) = n*(n^3 - n + 2)/2.

0, 1, 8, 39, 124, 305, 636, 1183, 2024, 3249, 4960, 7271, 10308, 14209, 19124, 25215, 32656, 41633, 52344, 64999, 79820, 97041, 116908, 139679, 165624, 195025, 228176, 265383, 306964, 353249, 404580, 461311, 523808, 592449, 667624, 749735, 839196, 936433

Offset

0,3

References

T. A. Gulliver, Sequences from Cubes of Integers, Int. Math. Journal, 4 (2003), 439-445.

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n>4. - Harvey P. Dale, Sep 28 2012

From Elmo R. Oliveira, Sep 08 2025: (Start)

G.f.: x*(1 + 3*x + 9*x^2 - x^3)/(1-x)^5.

E.g.f.: x*(2 + 6*x + 6*x^2 + x^3)*exp(x)/2. (End)

Example

From Bruno Berselli, Oct 30 2017: (Start)
After 0:
1   =                     -(0) + (1);
8   =                 -(0 + 1) + (2 + 3 + 2^2);
39  =             -(0 + 1 + 2) + (3 + 4 + 5 + 6 + 7 + 8 + 3^2);
124 =         -(0 + 1 + 2 + 3) + (4 + 5 + 6 + 7 + ... + 15 + 4^2);
305 =     -(0 + 1 + 2 + 3 + 4) + (5 + 6 + 7 + 8 + ... + 24 + 5^2);
636 = -(0 + 1 + 2 + 3 + 4 + 5) + (6 + 7 + 8 + 9 + ... + 35 + 6^2), etc. (End)

Mathematica

Table[n (n^3 - n + 2)/2, {n, 0, 50}] (* Harvey P. Dale, Sep 28 2012 *)
(* Alternative: *)
LinearRecurrence[{5, -10, 10, -5, 1}, {0, 1, 8, 39, 124}, 50] (* Harvey P. Dale, Sep 28 2012 *)

Prog

(Magma) [n*(n^3-n+2)/2: n in [0..40]]; // Vincenzo Librandi, May 26 2011

Crossrefs

Sequence in context: A190097 A245135 A200157 * A163687 A060446 A318267

Adjacent sequences: A101371 A101372 A101373 * A101375 A101376 A101377

Keyword

nonn,easy,changed

Author

N. J. A. Sloane, Jan 15 2005

Status

approved