A168209 a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=3.

3, 8, 8, 13, 13, 18, 18, 23, 23, 28, 28, 33, 33, 38, 38, 43, 43, 48, 48, 53, 53, 58, 58, 63, 63, 68, 68, 73, 73, 78, 78, 83, 83, 88, 88, 93, 93, 98, 98, 103, 103, 108, 108, 113, 113, 118, 118, 123, 123, 128, 128, 133, 133, 138, 138, 143, 143, 148, 148, 153, 153, 158

Offset: 1

Author

Vincenzo Librandi, Nov 20 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).

Programs

Magma

I:=[3, 8, 8]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 28 2012

Mathematica

LinearRecurrence[{1, 1, -1}, {3, 8, 8}, 30] (* Vincenzo Librandi, Feb 28 2012 *)
nxt[{n_,a_}]:={n+1,5(n+1)-a+1}; Transpose[NestList[nxt,{1,3},70]][[2]] (* Harvey P. Dale, Jan 23 2013 *)

Formula

a(n) = (10*n + 7 + 5*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010

G.f.: x*(3+5*x-3*x^2)/((1+x)*(1-x)^2). - Bruno Berselli, Feb 28 2012

E.g.f.: (1/4)*(5 - 12*exp(x) + (7 + 10*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016