A168212 a(n) = 7*n - a(n-1) + 1 with n>1, a(1)=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, 207

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

From R. J. Mathar, Nov 22 2009: (Start)

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

a(n) = (9 + 14*n + 7*(-1)^n)/4.

G.f.: x*(4 + 7*x - 4*x^2)/((1+x)* (x-1)^2). (End)

E.g.f.: (1/4)*(7 - 16*exp(x) + (9 + 14*x)*exp(2*x))*exp(-x). - G. C. Greubel, Jul 15 2016

Mathematica

LinearRecurrence[{1, 1, -1}, {4, 11, 11}, 60] (* Vincenzo Librandi, Feb 28 2012 *)
Join[{4}, With[{c=LinearRecurrence[{2, -1}, {11, 18}, 50]}, Riffle[c, c]]] (* or *) With[{c=7*Range[0, 50]+4}, Rest[Riffle[c, c]]] (* Harvey P. Dale, May 09 2018 *)

Prog

(Magma) I:=[4, 11, 11]; [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: A330683 A020949 A210693 * A014449 A281387 A355608

Adjacent sequences: A168209 A168210 A168211 * A168213 A168214 A168215

Keyword

nonn,easy

Author

Vincenzo Librandi, Nov 20 2009

Status

approved