A168207 a(n) = 5*n - a(n-1) + 1 with n>1, a(1)=2.

2, 14, 7, 19, 12, 24, 17, 29, 22, 34, 27, 39, 32, 44, 37, 49, 42, 54, 47, 59, 52, 64, 57, 69, 62, 74, 67, 79, 72, 84, 77, 89, 82, 94, 87, 99, 92, 104, 97, 109, 102, 114, 107, 119, 112, 124, 117, 129, 122, 134, 127, 139, 132, 144, 137, 149, 142, 154, 147, 159, 152, 164

Offset

1,1

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 + 17 + 19*(-1)^n)/4. - Jon E. Schoenfield, Jun 24 2010

G.f.: x*(2+12*x-9*x^2)/((1+x)*(1-x)^2). - Bruno Berselli, Feb 28 2012

E.g.f.: (1/4)*(19 - 36*exp(x) + (17 + 10*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = 13/36 + sqrt((5+sqrt(5))/10)*Pi/5 - log(phi)/sqrt(5), where phi is the golden ratio (A001622). - Amiram Eldar, Feb 23 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {2, 14, 7}, 30] (* Vincenzo Librandi, Feb 28 2012 *)

Prog

(Magma) I:=[2, 14, 7]; [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

Crossrefs

Cf. A001622.

Sequence in context: A084677 A344115 A191995 * A082609 A271382 A158787

Adjacent sequences: A168204 A168205 A168206 * A168208 A168209 A168210

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved