A168390 a(n) = 1 + 8*floor(n/2).
1, 9, 9, 17, 17, 25, 25, 33, 33, 41, 41, 49, 49, 57, 57, 65, 65, 73, 73, 81, 81, 89, 89, 97, 97, 105, 105, 113, 113, 121, 121, 129, 129, 137, 137, 145, 145, 153, 153, 161, 161, 169, 169, 177, 177, 185, 185, 193, 193, 201, 201, 209, 209, 217, 217, 225, 225, 233, 233
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
[1+8*Floor(n/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013
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Mathematica
RecurrenceTable[{a[1]==1,a[n]==8n-a[n-1]-6},a,{n,60}] (* or *) LinearRecurrence[{1,1,-1},{1,9,9},60] (* or *) With[{c=Table[8n+1,{n,0,40}]},Rest[Riffle[c,c]]] (* Harvey P. Dale, Jul 28 2012 *) Table[1 + 8 Floor[n/2], {n, 60}] (* Bruno Berselli, Sep 18 2013 *) CoefficientList[Series[(1 + 8 x - x^2)/((1 + x) (x - 1)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 18 2013 *)
Formula
a(n) = 8*n - a(n-1) - 6, with n>1, a(1)=1.
a(1)=1, a(2)=9, a(3)=9; for n>3, a(n) = a(n-1) + a(n-2) - a(n-3). - Harvey P. Dale, Jul 28 2012
G.f.: x*(1 + 8*x - x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013
E.g.f.: (2 - exp(x) + (4*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016
Extensions
New definition by Vincenzo Librandi, Sep 18 2013