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Search: id:A117110
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| A117110 |
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The (1,1)-entry of the vector v[n]=Mv[n-1], where M is the 3 x 3 matrix [[0,-1/r,r],[ -1/r,-2/r,1],[r,1,2+2/r]], r being the golden ratio, and v[0] is the column matrix [0,1,1]. |
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+0
2
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| 0, 1, 7, 22, 100, 376, 1552, 6112, 24640, 98176, 393472, 1572352, 6292480, 25163776, 100667392, 402644992, 1610629120, 6442418176, 25769869312, 103079084032, 412317122560, 1649266917376, 6597070815232, 26388276969472
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OFFSET
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0,3
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COMMENT
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Characteristic polynomial of the matrix M is x(x^2-2x-8).
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FORMULA
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Recurrence relation: a(n)=2a(n-1)+8a(n-2) for n>=3; a(0)=0,a(1)=1,a(2)=7.
O.g.f.: -x*(1+5*x)/((2*x+1)*(4*x-1)). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 05 2007
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MAPLE
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a[0]:=0: a[1]:=1: a[2]:=7: for n from 3 to 26 do a[n]:=2*a[n-1]+8*a[n-2] od: seq(a[n], n=0..26);
with(linalg): r:=(1+sqrt(5))/2: M:=matrix(3, 3, [0, -1/r, r, -1/r, -2/r, 1, r, 1, 2+2/r]): v[0]:=matrix(3, 1, [0, 1, 1]): for n from 1 to 26 do v[n]:=simplify(multiply(M, v[n-1])) od: seq(simplify(rationalize(v[n][1, 1])), n=0..26);
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CROSSREFS
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Sequence in context: A101289 A085287 A041913 this_sequence A027838 A000835 A087184
Adjacent sequences: A117107 A117108 A117109 this_sequence A117111 A117112 A117113
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 18 2006
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EXTENSIONS
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Edited by njas, May 13 2006
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