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 A111733 a(n) = a(n-1) + a(n-2) + 7 where a(0) = a(1) = 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 11 10:08 EDT 2024. Contains 375827 sequences. (Running on oeis4.)