A168392 a(n) = 5 + 8*floor((n-1)/2).

5, 5, 13, 13, 21, 21, 29, 29, 37, 37, 45, 45, 53, 53, 61, 61, 69, 69, 77, 77, 85, 85, 93, 93, 101, 101, 109, 109, 117, 117, 125, 125, 133, 133, 141, 141, 149, 149, 157, 157, 165, 165, 173, 173, 181, 181, 189, 189, 197, 197, 205, 205, 213, 213, 221, 221, 229, 229

Offset: 1

Author

Vincenzo Librandi, Nov 24 2009

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Crossrefs

Cf. A004770, A168379.

Programs

Magma

[5+8*Floor((n-1)/2): n in [1..70]]; // Vincenzo Librandi, Sep 18 2013

Mathematica

RecurrenceTable[{a[1]==5,a[n]==8n-a[n-1]-6},a,{n,80}] (* or *) LinearRecurrence[{1,1,-1},{5,5,13},80] (* or *) With[{c= LinearRecurrence[ {2,-1},{5,13},40]}, Riffle[c,c]] (* Harvey P. Dale, Jan 27 2013 *)
Table[5 + 8 Floor[(n - 1)/2], {n, 60}] (* Bruno Berselli, Sep 18 2013 *)
CoefficientList[Series[(5 + 3 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)=5.

a(1) = 5, a(2)=5, a(3)=13; for n>3, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Jan 27 2013

G.f.: x*(5 + 3*x^2)/((1+x)*(x-1)^2). - Vincenzo Librandi, Sep 18 2013

E.g.f.: (-2 + 3*exp(x) + (4*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 19 2016

a(n) = A168379(n) - 2. - Filip Zaludek, Nov 01 2016

Extensions

New definition by Vincenzo Librandi, Sep 18 2013