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A120758
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The (1,3)-entry in the matrix M^n, where M is the 3 X 3 matrix [0,2,1; 2,1,2; 1,2,2] (n>=1).
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1
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1, 6, 25, 116, 517, 2338, 10517, 47400, 213481, 961726, 4332145, 19515036, 87908397, 395998298, 1783838637, 8035595600, 36197658961, 163058307446, 734522939465, 3308779311556, 14904940203477, 67141752851858
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n)/a(n-1) tends to 4.50466435...an eigenvalue of M and a root to the characteristic polynomial x^3 - 3x^2 - 7x + 1.
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LINKS
| Title?, Title?
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FORMULA
| a(n)=3a(n-1)+7a(n-2)-a(n-3) (follows from the minimal polynomial of the matrix M).
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EXAMPLE
| a(7)=10517 because M^7= [6682,9842,10517;9842,14401,15438;10517,15438,16524].
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MAPLE
| with(linalg): M[1]:=matrix(3, 3, [0, 2, 1, 2, 1, 2, 1, 2, 2]): for n from 2 to 25 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][3, 1], n=1..25);
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CROSSREFS
| Cf. A120757.
Sequence in context: A048875 A094669 A100296 * A179603 A153481 A099359
Adjacent sequences: A120755 A120756 A120757 * A120759 A120760 A120761
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Jul 01 2006
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EXTENSIONS
| Corrected by T. D. Noe (noe(AT)sspectra.com), Nov 07 2006
Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 04 2006
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