A111733 a(n) = a(n-1) + a(n-2) + 7 where a(0) = a(1) = 1.

1, 1, 9, 17, 33, 57, 97, 161, 265, 433, 705, 1145, 1857, 3009, 4873, 7889, 12769, 20665, 33441, 54113, 87561, 141681, 229249, 370937, 600193, 971137, 1571337, 2542481, 4113825, 6656313, 10770145, 17426465, 28196617, 45623089, 73819713, 119442809

Offset

0,3

Comments

This is the sequence A(1,1;1,1;7)of the family of sequences [a,b:c,d:k] considered by Gary Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. - Wolfdieter Lang, Oct 17 2010

Links

Table of n, a(n) for n=0..35.

Wolfdieter Lang, Notes on certain inhomogeneous three term recurrences.

Index entries for linear recurrences with constant coefficients, signature (2,0,-1)

Formula

From R. J. Mathar, Jul 08 2009: (Start)

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

a(n) = 8*A000045(n+1) - 7 = 2*a(n-1) - a(n-3). (End)

a(n+1) - a(n) = A022091(n). - R. J. Mathar, Apr 22 2013

Example

a(2) = a(0) + a(1) + 7 = 1 + 1 + 7 = 9, which is the third term in the sequence.

Mathematica

a[0] := 1; a[1] := 1; a[n_] := a[n - 1] + a[n - 2] + 7; Table[a[n], {n, 0, 30}] (* Stefan Steinerberger, Mar 10 2006 *)
LinearRecurrence[{2, 0, -1}, {1, 1, 9}, 40] (* Vincenzo Librandi, Sep 16 2015 *)

Prog

(Magma) I:=[1, 1, 9]; [n le 3 select I[n] else 2*Self(n-1)-Self(n-3): n in [1..40]]; // Vincenzo Librandi, Sep 16 2015

Crossrefs

Sequence in context: A335796 A260477 A275543 * A127193 A262453 A197344

Adjacent sequences: A111730 A111731 A111732 * A111734 A111735 A111736

Keyword

nonn,easy

Author

Parthasarathy Nambi, Nov 18 2005

Extensions

More terms from Stefan Steinerberger, Mar 10 2006

More terms from Brian Lauer (bel136(AT)psu.edu), Apr 05 2006

Status

approved