A155753 a(n) = (n^3 - n + 9)/3.

3, 5, 11, 23, 43, 73, 115, 171, 243, 333, 443, 575, 731, 913, 1123, 1363, 1635, 1941, 2283, 2663, 3083, 3545, 4051, 4603, 5203, 5853, 6555, 7311, 8123, 8993, 9923, 10915, 11971, 13093, 14283, 15543, 16875, 18281, 19763, 21323, 22963

Offset

1,1

Links

Bruno Berselli, Table of n, a(n) for n = 1..10000.

Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).

Formula

a(n) = a(n-1) + n*(n-1), with a(1)=3 .

From Bruno Berselli, Jun 21 2010: (Start)

G.f.: x*(3 -9*x +11*x^2 -3*x^3)/(1-x)^4.

a(n) + a(n-1) = 2*A153057(n-1) (n>1).

a(n) + A000217(n) = A153057(n) (n>0).

a(n) - 4*a(n-1) + 6*a(n-2) - 4*a(n-3) + a(n-4) = 0 with n>4.

a(n) = 3 + A007290(n+1) = (n^3 - n + 9)/3. (End)

E.g.f.: (1/3)*(-9 + (9 + 3*x^2 + x^3)*exp(x)). - G. C. Greubel, Jun 05 2021

Mathematica

f[n_]:=(n^3 -n +9)/3; f[Range[1, 100]] (* Vladimir Joseph Stephan Orlovsky, Feb 10 2011*)
LinearRecurrence[{4, -6, 4, -1}, {3, 5, 11, 23}, 50] (* Harvey P. Dale, Oct 20 2011 *)

Prog

(PARI) a(n)=(n^3-n)/3+3 \\ Charles R Greathouse IV, Jan 11 2012
(Sage) [(n^3 -n +9)/3 for n in (1..50)] # G. C. Greubel, Jun 05 2021

Crossrefs

Cf. A000217, A007290, A153057.

Sequence in context: A109927 A347287 A146276 * A133914 A169913 A260239

Adjacent sequences: A155750 A155751 A155752 * A155754 A155755 A155756

Keyword

nonn,easy

Author

Vincenzo Librandi, Jan 26 2009

Extensions

Entries confirmed by John W. Layman, Jun 17 2010

Edited by Bruno Berselli, Aug 12 2010

New name from Charles R Greathouse IV, Jan 11 2012

Status

approved