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A111733
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a(n) = a(n-1) + a(n-2) + 7 where a(0) = a(1) = 1.
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0
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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; internal format)
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OFFSET
| 0,3
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COMMENTS
| This is the sequence A(1,1;1,1;7)of the family of sequences [a,b:c,d:k] considered by G. Detlefs, and treated as A(a,b;c,d;k) in the W. Lang link given below. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 17 2010]
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LINKS
| W. Lang, Notes on certain inhomogeneous three term recurrences. [From Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Oct 17 2010]
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FORMULA
| 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). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 08 2009]
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EXAMPLE
| a(2) = a(0) + a(1) + 7 = 1 + 1 + 7 = 9, which is the third term in the sequence.
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MATHEMATICA
| a[0] := 1; a[1] := 1; a[n_] := a[n - 1] + a[n - 2] + 7; Table[a[n], {n, 0, 30}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 10 2006
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CROSSREFS
| Sequence in context: A014004 A090994 A164887 * A127193 A197344 A146236
Adjacent sequences: A111730 A111731 A111732 * A111734 A111735 A111736
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KEYWORD
| nonn
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AUTHOR
| Parthasarathy Nambi (PachaNambi(AT)yahoo.com), Nov 18 2005
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EXTENSIONS
| More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Mar 10 2006
More terms from Brian Lauer (bel136(AT)psu.edu), Apr 05 2006
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