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Search: id:A102105
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| A102105 |
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(1/4) [19*5^n - 16*3^n + 1 ]. |
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+0
1
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| 1, 12, 83, 486, 2645, 13872, 71303, 362346, 1829225, 9198612, 46150523, 231225006, 1157542205, 5791962552, 28972567343, 144901100466, 724620293585, 3623445841692, 18118262329763, 90594411012726, 452981353155365
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum of the entries in the last row of the 3 X 3 matrix M^n, where M={{1 0 0}{2 3 0 }{ 3 4 5}}.
Sum of the entries in the second row of M^n = A048473(n).
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FORMULA
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a(n) = 9a(n-1) - 23a(n-2) + 15a(n-3), a(0)=1,a(1)=12,a(2)=83 (derived from the minimal polynomial of the matrix M).
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EXAMPLE
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a(4) = 2645 = 9*486 - 23*83 + 15*12 = 9*a(3) - 23*a(2) + 15*a(1).
a(4) = 2645 since M^4 * [1 1 1] = [1 161 2645], where 161 = A048473(4).
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MAPLE
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with(linalg): M[1]:=matrix(3, 3, [1, 0, 0, 2, 3, 0, 3, 4, 5]): for n from 2 to 23 do M[n]:=multiply(M[1], M[n-1]) od: 1, seq(multiply(M[n], matrix(3, 1, [1, 1, 1]))[3, 1], n=1..23);
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CROSSREFS
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Cf. A000326, A094727, A048473.
Sequence in context: A163020 A164300 A175037 this_sequence A026949 A165127 A075476
Adjacent sequences: A102102 A102103 A102104 this_sequence A102106 A102107 A102108
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Dec 30 2004
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EXTENSIONS
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Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 02 2006
New definition from Ralf Stephan, May 17 2007
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