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Search: id:A120757
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| A120757 |
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The (1,1)-entry of the matrix M^n, where M is the 3 X 3 matrix [0,1,1; 1,1,2; 1,2,2](n>=1). |
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3
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| 0, 2, 7, 29, 117, 474, 1919, 7770, 31460, 127379, 515747, 2088217, 8455018, 34233669, 138609296, 561217582, 2272323599, 9200450421, 37251863241, 150829715006, 610697048403, 2472661868474, 10011603514040, 40536155064419
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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a(n)/a(n-1) tends to 4.0489173...an eigenvalue of M and a root to the characteristic polynomial x^3 - 3x^2 - 4x - 1.
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LINKS
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Author?, Title?
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FORMULA
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a(n)=3a(n-1)+4a(n-2)+a(n-3) (follows from the minimal polynomial of the matrix M).
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EXAMPLE
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a(7)=1919 because M^7= [1919,3458,4312;3458,6231,7770;4312,7770,9689].
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MAPLE
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with(linalg): M[1]:=matrix(3, 3, [0, 1, 1, 1, 1, 2, 1, 2, 2]): for n from 2 to 25 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][1, 1], n=1..25);
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CROSSREFS
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Sequence in context: A166940 A166939 A155186 this_sequence A134169 A052961 A150662
Adjacent sequences: A120754 A120755 A120756 this_sequence A120758 A120759 A120760
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Jul 01 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Dec 03 2006
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