A035104 First differences give (essentially) A028242.
1, 4, 9, 13, 19, 24, 31, 37, 45, 52, 61, 69, 79, 88, 99, 109, 121, 132, 145, 157, 171, 184, 199, 213, 229, 244, 261, 277, 295, 312, 331, 349, 369, 388, 409, 429, 451, 472, 495, 517, 541, 564, 589, 613, 639, 664, 691, 717, 745, 772, 801, 829, 859, 888, 919
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (2,0,-2,1).
Programs
-
Magma
[(5+3*(-1)^n+28*n+2*n^2)/8: n in [0..60]]; // Vincenzo Librandi, Oct 20 2013
-
Mathematica
CoefficientList[Series[(3 x^3 - x^2 - 2 x - 1)/((x - 1)^3 (x + 1)), {x, 0, 60}], x] (* Vincenzo Librandi, Oct 20 2013 *)
Formula
From Colin Barker, Mar 04 2013: (Start)
a(n) = (5+3*(-1)^n+28*n+2*n^2)/8.
a(n) = 2*a(n-1)-2*a(n-3)+a(n-4).
G.f.: (3*x^3-x^2-2*x-1) / ((x-1)^3*(x+1)). (End)
Sum_{n>=0} 1/a(n) = 983/990 + tan(3*sqrt(5)*Pi/2)*Pi/(3*sqrt(5)) - cot(2*sqrt(3)*Pi)*Pi/(4*sqrt(3)). - Amiram Eldar, Sep 24 2022
Extensions
More terms from Vincenzo Librandi, Oct 20 2013