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Search: id:A104100
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| A104100 |
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First entry of the vector (M^n)v, where M is the 4 x 4 matrix [[0, 1, 3, 8], [0, 0, 1, 5], [0, 0, 0, 1], [1, 2, 1, 1]] and v is the column vector [[0, 1, 1, 2]. |
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1
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| 0, 20, 57, 434, 1717, 10553, 47573, 265684, 1276818, 6811097, 33775052, 176219759, 887333535, 4580070573, 23235380380, 119306276376, 607466542861, 3111219668378, 15869382126877, 81176527531045, 414414451168349
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Characteristic polynomial of the matrix M is x^4-x^3-19x^2-10x-1.
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FORMULA
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Recurrence relation: a(n)=a(n-1)+19a(n-2)+10a(n-3)+a(n-4) for n>=4; a(0)=0, a(1)=20, a(2)=57, a(3)=434.
O.g.f.: x*(-20-37*x+3*x^2)/(-1+x+19*x^2+10*x^3+x^4). - 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]:=20:a[2]:=57:a[3]:=434: for n from 4 to 22 do a[n]:=a[n-1]+19*a[n-2]+10*a[n-3]+a[n-4] od: seq(a[n], n=0..22);
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MATHEMATICA
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Ms = {{0, 1, 3, 8}, {0, 0, 1, 5}, {0, 0, 0, 1}, {1, 2, 1, 1}}; z[0] = {0, 1, 1, 2}; z[n_] := z[n] = Ms.z[n - 1] a=Table[z[n][[1]], {n, 0, 50}]
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CROSSREFS
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Sequence in context: A109806 A012483 A051872 this_sequence A069132 A124713 A126374
Adjacent sequences: A104097 A104098 A104099 this_sequence A104101 A104102 A104103
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KEYWORD
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nonn
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 31 2005
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), May 20 2006
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