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
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
Programs
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Magma
[(6*n+7*(-1)^n+3)/2: n in [1..80]]; // Vincenzo Librandi, Sep 13 2013
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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 *) -
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
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