A168282 (10*n + 5*(-1)^n - 1)/4.

1, 6, 6, 11, 11, 16, 16, 21, 21, 26, 26, 31, 31, 36, 36, 41, 41, 46, 46, 51, 51, 56, 56, 61, 61, 66, 66, 71, 71, 76, 76, 81, 81, 86, 86, 91, 91, 96, 96, 101, 101, 106, 106, 111, 111, 116, 116, 121, 121, 126, 126, 131, 131, 136, 136, 141, 141, 146, 146, 151, 151, 156

Offset: 1

Author

Vincenzo Librandi, Nov 22 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. A016861, A168278, A168457, A168459.

Programs

Magma

[n le 1 select (n) else 5*n-Self(n-1)-3: n in [1..70]]; // Vincenzo Librandi, Sep 16 2013

Mathematica

RecurrenceTable[{a[1]==1,a[n]==5n-a[n-1]-3},a,{n,70}] (* or *) LinearRecurrence[{1,1,-1},{1,6,6},70] (* Harvey P. Dale, Jun 17 2013 *)
Table[5 n/2 + 5 (-1)^n/4 - 1/4, {n, 70}] (* Bruno Berselli, Sep 16 2013 *)
CoefficientList[Series[(1 + 5 x - x^2) / ((1 + x) (1 - x)^2), {x, 0, 70}], x] (* Vincenzo Librandi, Sep 16 2013 *)

PARI

a(n)=5*n/2+5*(-1)^n/4-1/4 \\ Charles R Greathouse IV, Oct 16 2015

Formula

a(n) = 5*n - a(n-1) - 3 for n>1, a(1)=1.

a(1)=1, a(2)=6, a(3)=6; for n>3, a(n) = a(n-1) +a(n-2) -a(n-3). - Harvey P. Dale, Jun 17 2013

From Bruno Berselli, Sep 16 2013: (Start)

G.f.: x*(1 + 5*x - x^2)/((1+x)*(1-x)^2).

a(n) = A168457(n)/2.

a(n) = A168278(n) - 1.

a(n) = ( A168459(n) + 1 )/2. (End)

E.g.f.: (1/4)*(5 - 4*exp(x) + (2*x - 1)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 16 2016

Extensions

New definition by Bruno Berselli, Sep 16 2013