A168205 a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=2.

2, 7, 6, 11, 10, 15, 14, 19, 18, 23, 22, 27, 26, 31, 30, 35, 34, 39, 38, 43, 42, 47, 46, 51, 50, 55, 54, 59, 58, 63, 62, 67, 66, 71, 70, 75, 74, 79, 78, 83, 82, 87, 86, 91, 90, 95, 94, 99, 98, 103, 102, 107, 106, 111, 110, 115, 114, 119, 118, 123, 122, 127, 126, 131, 130

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) = (4*n + 3 + 3*(-1)^n)/2. - Jon E. Schoenfield, Jun 24 2010

a(n) = a(n-1) + a(n-2) - a(n-3), a(1)=2, a(2)=7, a(3)=6. - Harvey P. Dale, Feb 04 2012

G.f.: x*(2 + 5*x - 3*x^2)/((-1+x)^2*(1+x)). - Harvey P. Dale, Feb 04 2012

E.g.f.: (1/2)*(3 - 6*exp(x) + (3 + 4*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

Sum_{n>=1} (-1)^(n+1)/a(n) = 1/3 + Pi/8 - log(2)/4. - Amiram Eldar, Feb 23 2023

Mathematica

RecurrenceTable[{a[1]==2, a[n]==4n-a[n-1]+1}, a, {n, 70}] (* or *) LinearRecurrence[{1, 1, -1}, {2, 7, 6}, 70] (* Harvey P. Dale, Feb 04 2012 *)

Prog

(Magma) I:=[2, 7, 6]; [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

Sequence in context: A320871 A154200 A089417 * A265495 A338041 A365007

Adjacent sequences: A168202 A168203 A168204 * A168206 A168207 A168208

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved