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

0,2

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).

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

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 *)

Prog

(Magma) [(5+3*(-1)^n+28*n+2*n^2)/8: n in [0..60]]; // Vincenzo Librandi, Oct 20 2013

Crossrefs

Cf. A004652, A035106, A035107.

Sequence in context: A312978 A312979 A312980 * A141224 A064423 A312981

Adjacent sequences: A035101 A035102 A035103 * A035105 A035106 A035107

Keyword

nonn,easy

Author

N. J. A. Sloane.

Extensions

More terms from Vincenzo Librandi, Oct 20 2013

Status

approved