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Search: id:A122883
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| A122883 |
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The (1,3)-entry in the 3 X 3 matrix M^n, where M=[1,1,1; 4,2,1; 9,3,1] (n>=1). |
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4
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| 1, 3, 23, 123, 739, 4263, 24935, 145155, 846379, 4932351, 28749263, 167560155, 976617811, 5692134423, 33176213303, 193365096243, 1127014462459, 6568721481903, 38285314822175, 223143166664715, 1300573686738979
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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a(n)=4a(n-1)+11a(n-2)-2a(n-3) (derived from the minimal polynomial of the matrix M).
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EXAMPLE
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a(6)=4263 because M^3=[13742,6930,4263; 25053,12671,7819; 41034,20790,12853]; alternatively, a(6)=4a(5)+11a(4)-2a(3)=4*729+11*123-2*23=4263.
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MAPLE
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with(linalg): M[1]:=matrix(3, 3, [1, 1, 1, 4, 2, 1, 9, 3, 1]): for n from 2 to 25 do M[n]:=multiply(M[1], M[n-1]) od: seq(M[n][1, 3], n=1..25);
a[1]:=1:a[2]:=3:a[3]:=23:for n from 4 to 25 do a[n]:=4*a[n-1]+11*a[n-2]-2*a[n-3] od: seq(a[n], n=1..25);
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CROSSREFS
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Cf. A122884, A122885, A122886.
Adjacent sequences: A122880 A122881 A122882 this_sequence A122884 A122885 A122886
Sequence in context: A039506 A006557 A081628 this_sequence A091055 A031970 A049164
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KEYWORD
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nonn
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AUTHOR
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Gary W. Adamson and Roger L. Bagula (qntmpkt(AT)yahoo.com), Sep 17 2006
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EXTENSIONS
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Edited by njas, Dec 04 2006
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