A166521 a(n) = (6*n + 7*(-1)^n + 3)/2.

1, 11, 7, 17, 13, 23, 19, 29, 25, 35, 31, 41, 37, 47, 43, 53, 49, 59, 55, 65, 61, 71, 67, 77, 73, 83, 79, 89, 85, 95, 91, 101, 97, 107, 103, 113, 109, 119, 115, 125, 121, 131, 127, 137, 133, 143, 139, 149, 145, 155, 151, 161, 157, 167, 163, 173, 169, 179, 175, 185

Offset

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 6*n - a(n-1), for n > 1, with a(1) = 1.

G.f.: x*(1+10*x-5*x^2) / ((1+x)*(1-x)^2). - R. J. Mathar, Mar 08 2011

From G. C. Greubel, May 16 2016: (Start)

E.g.f.: (1/2)*(7*exp(-x) + 3*(1+2*x)*exp(x) -10).

a(n) = a(n-1) + a(n-2) - a(n-3). (End)

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/5 + Pi/(2*sqrt(3)). - Amiram Eldar, Feb 24 2023

Mathematica

Table[(6 n + 7 (-1)^n + 3)/2, {n, 60}] (* Vincenzo Librandi, Sep 13 2013 *)
LinearRecurrence[{1, 1, -1}, {1, 11, 7}, 90] (* Harvey P. Dale, Apr 29 2018 *)

Prog

(Magma) [(6*n+7*(-1)^n+3)/2: n in [1..80]]; // Vincenzo Librandi, Sep 13 2013
(SageMath)
def A166521(n): return 3*n -2 +7*((n+1)%2)
[A166521(n) for n in range(1, 101)] # G. C. Greubel, Aug 03 2024

Crossrefs

Cf. A166519, A166520, A166522, A166523, A166524, A166525, A166526.

Sequence in context: A265765 A187563 A089487 * A187866 A206419 A250032

Adjacent sequences: A166518 A166519 A166520 * A166522 A166523 A166524

Keyword

nonn,easy

Author

Vincenzo Librandi, Oct 16 2009

Status

approved