A168203 a(n) = 4*n - a(n-1) + 1 with n>1, a(1)=0.

0, 9, 4, 13, 8, 17, 12, 21, 16, 25, 20, 29, 24, 33, 28, 37, 32, 41, 36, 45, 40, 49, 44, 53, 48, 57, 52, 61, 56, 65, 60, 69, 64, 73, 68, 77, 72, 81, 76, 85, 80, 89, 84, 93, 88, 97, 92, 101, 96, 105, 100, 109, 104, 113, 108, 117, 112, 121, 116, 125, 120, 129, 124, 133, 128, 137

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) = (4*n + 3 + 7*(-1)^n)/2. - Jon E. Schoenfield, Jun 24 2010

G.f.: x^2*(9-5*x)/((1+x)*(1-x)^2). - Vincenzo Librandi, Feb 28 2012

E.g.f.: (1/2)*(7 - 10*exp(x) + (3 + 4*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

Sum_{n>=2} (-1)^(n+1)/a(n) = 6/5 - Pi/8 - 3*log(2)/4. - Amiram Eldar, Feb 23 2023

Mathematica

LinearRecurrence[{1, 1, -1}, {0, 9, 4}, 60] (* Vincenzo Librandi, Feb 28 2012 *)
nxt[{n_, a_}]:={n+1, 4n-a+5}; NestList[nxt, {1, 0}, 70][[;; , 2]] (* Harvey P. Dale, Mar 04 2023 *)

Prog

(Magma) I:=[0, 9, 4]; [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

Sequence in context: A255642 A088701 A153698 * A248310 A133597 A075066

Adjacent sequences: A168200 A168201 A168202 * A168204 A168205 A168206

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved