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

Author

Parthasarathy Nambi, Nov 18 2005

Keywords

• nonn
• easy

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

Examples

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

Links

• Wolfdieter Lang, Notes on certain inhomogeneous three term recurrences.
• Index entries for linear recurrences with constant coefficients, signature (2,0,-1)

Programs

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

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 *)

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

Extensions

More terms from Stefan Steinerberger, Mar 10 2006

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