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

1,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

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

a(n) = A168381(n) - 1 = A168378(n) - 2. - Bruno Berselli, Sep 18 2013

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

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 *)

Prog

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

Crossrefs

Cf. A017077, A168378, A168381.

Sequence in context: A144418 A003885 A344335 * A333151 A321659 A040073

Adjacent sequences: A168387 A168388 A168389 * A168391 A168392 A168393

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 24 2009

Extensions

New definition by Vincenzo Librandi, Sep 18 2013

Status

approved