A168206 a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=0.

0, 11, 5, 16, 10, 21, 15, 26, 20, 31, 25, 36, 30, 41, 35, 46, 40, 51, 45, 56, 50, 61, 55, 66, 60, 71, 65, 76, 70, 81, 75, 86, 80, 91, 85, 96, 90, 101, 95, 106, 100, 111, 105, 116, 110, 121, 115, 126, 120, 131, 125, 136, 130, 141, 135, 146, 140, 151, 145, 156, 150, 161

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) = (10*n + 7 + 17*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010

G.f.: x^2*(11-6*x)/((1+x)*(1-x)^2). - Vincenzo Librandi, Feb 28 2012

E.g.f.: (1/4)*(17 - 24*exp(x) + (7 + 10*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

Sum_{n>=2} (-1)^(n+1)/a(n) = 7/6 - log(5)/4 - log(phi)/(2*sqrt(5)) - sqrt(1+2/sqrt(5))*Pi/10, where phi is the golden ratio (A001622). - Amiram Eldar, Feb 23 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {0, 11, 5}, 30] (* Vincenzo Librandi, Feb 28 2012 *)

Prog

(Magma) I:=[0, 11, 5]; [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

Crossrefs

Cf. A001622.

Sequence in context: A303978 A085716 A127820 * A120831 A253254 A373730

Adjacent sequences: A168203 A168204 A168205 * A168207 A168208 A168209

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved