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A107332
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The (1,3)-entry of the matrix M^n, where M is the 5x5 matrix [[0,1,0,0,0],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,1],[1,0,-1,1,1]].
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1
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0, 1, 0, 0, -1, -1, -1, -1, -1, -2, -3, -5, -7, -10, -14, -20, -29, -42, -61, -88, -127, -183, -264, -381, -550, -794, -1146, -1654, -2387, -3445, -4972, -7176, -10357, -14948, -21574, -31137, -44939, -64859, -93609, -135103, -194990, -281423, -406169, -586211, -846060, -1221092, -1762364
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,10
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COMMENTS
| Characteristic polynomial of the matrix M is x^5-x^4-x^3+x^2-1.
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FORMULA
| Recurrence relation: a(n)=a(n-1)+a(n-2)-a(n-3)+a(n-5) for n>=5; a(0)=0,a(1)=1,a(2)=a(3)=0,a(4)=-1.
O.g.f.: x^2*(-1+x+x^2)/(-1+x+x^2-x^3+x^5). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Dec 02 2007
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MAPLE
| a[0]:=0:a[1]:=1:a[2]:=0:a[3]:=0:a[4]:=-1: for n from 5 to 46 do a[n]:=a[n-1]+a[n-2]-a[n-3]+a[n-5] od: seq(a[n], n=0..46);
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MATHEMATICA
| M = {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 0, -1, 1, 1}} threes = Table[Abs[MatrixPower[M, i][[1, 3]]], {i, 1, 50}]
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CROSSREFS
| Sequence in context: A000701 A123975 A094984 * A002062 A005688 A120446
Adjacent sequences: A107329 A107330 A107331 * A107333 A107334 A107335
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KEYWORD
| sign
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 08 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 13 2006
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