A168373 a(n) = 7*n - a(n-1) - 6 with n>1, a(1)=4.

4, 4, 11, 11, 18, 18, 25, 25, 32, 32, 39, 39, 46, 46, 53, 53, 60, 60, 67, 67, 74, 74, 81, 81, 88, 88, 95, 95, 102, 102, 109, 109, 116, 116, 123, 123, 130, 130, 137, 137, 144, 144, 151, 151, 158, 158, 165, 165, 172, 172, 179, 179, 186, 186, 193, 193, 200, 200, 207

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).

Programs

Magma

I:=[4, 4, 11]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..60]]; // Vincenzo Librandi, Feb 28 2012

Mathematica

LinearRecurrence[{1, 1, -1}, {4, 4, 11}, 60] (* Vincenzo Librandi, Feb 28 2012 *)

PARI

a(n)=([0,1,0; 0,0,1; -1,1,1]^(n-1)*[4;4;11])[1,1] \\ Charles R Greathouse IV, Jul 19 2016

Formula

a(n) = A168212(n-1), n>1. - R. J. Mathar, Nov 25 2009

From G. C. Greubel, Jul 19 2016: (Start)

a(n) = (14*n - 7 (-1)^n - 5)/4.

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(4 + 3*x^2)/((1+x)*(1 - x)^2).

E.g.f.: (1/4)*(-7 + 12*exp(x) + (14*x - 5)*exp(2*x))*exp(-x). (End)