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
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).
Programs
-
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 *)
-
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
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) - 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
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