A168332 a(n) = 6 + 7 * floor((n-1)/2).
6, 6, 13, 13, 20, 20, 27, 27, 34, 34, 41, 41, 48, 48, 55, 55, 62, 62, 69, 69, 76, 76, 83, 83, 90, 90, 97, 97, 104, 104, 111, 111, 118, 118, 125, 125, 132, 132, 139, 139, 146, 146, 153, 153, 160, 160, 167, 167, 174, 174, 181, 181, 188, 188, 195, 195, 202, 202, 209
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 6 else 7*n-Self(n-1)-2: n in [1..70]]; // Vincenzo Librandi, Sep 17 2013
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Mathematica
Table[6 + 7 Floor[(n - 1)/2], {n, 60}] (* Bruno Berselli, Sep 17 2013 *) CoefficientList[Series[(6 + x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 17 2013 *) LinearRecurrence[{1,1,-1},{6,6,13},60] (* or *) With[{c=NestList[ #+7&,6,30]}, Riffle[c,c]] (* Harvey P. Dale, Aug 29 2015 *)
Formula
a(n) = 7*n - a(n-1) - 2, with n>1, a(1)=6.
G.f.: x*(6 + x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 17 2013
a(n) = a(n-1) +a(n-2) -a(n-3). - Vincenzo Librandi, Sep 17 2013
E.g.f.: (1/2)*(2 + (7*x - 2)*cosh(x) + (7*x + 5)*sinh(x)). - G. C. Greubel, Jul 18 2016
Extensions
Definition reformulated by Bruno Berselli at the suggestion of Joerg Arndt and using its formula, Sep 17 2013