A168277 a(n) = 2*n - (-1)^n - 2.
1, 1, 5, 5, 9, 9, 13, 13, 17, 17, 21, 21, 25, 25, 29, 29, 33, 33, 37, 37, 41, 41, 45, 45, 49, 49, 53, 53, 57, 57, 61, 61, 65, 65, 69, 69, 73, 73, 77, 77, 81, 81, 85, 85, 89, 89, 93, 93, 97, 97, 101, 101, 105, 105, 109, 109, 113, 113, 117, 117, 121, 121, 125, 125, 129, 129
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
[n eq 1 select 1 else 4*n-Self(n-1)-6: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013
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Mathematica
CoefficientList[Series[(1 + 3 x^2) / ((1 + x) (x - 1)^2), {x, 0, 80}], x] (* Vincenzo Librandi, Sep 16 2013 *) Table[2 n - (-1)^n - 2, {n, 70}] (* Bruno Berselli, Sep 17 2013 *) LinearRecurrence[{1,1,-1},{1,1,5},70] (* Harvey P. Dale, Aug 25 2015 *) -
PARI
a(n)=2*n-(-1)^n-2 \\ Charles R Greathouse IV, Oct 07 2015
Formula
a(n) = 4*n - a(n-1) - 6, with n>1, a(1)=1.
a(n) = A163980(n-1), n>1. - R. J. Mathar, Nov 25 2009
G.f.: x*(1 + 3*x^2)/( (1+x)*(x-1)^2 ). - R. J. Mathar, Jul 15 2013
a(n) = A168276(n) - 1. - Vincenzo Librandi, Sep 17 2013
a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 17 2013
E.g.f.: (-1 + 3*exp(x) + 2*(x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016
Sum_{n>=1} 1/a(n)^2 = Pi^2/8 + G, where G is Catalan's constant (A006752). - Amiram Eldar, Aug 21 2022
Extensions
New definition from Bruno Berselli, Sep 17 2013