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A123941
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The (1,2)-entry in the 3 X 3 matrix M^n, where M = {{2, 1, 1}, {1, 1, 0}, {1, 0, 0}}.
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0
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0, 1, 3, 9, 26, 75, 216, 622, 1791, 5157, 14849, 42756, 123111, 354484, 1020696, 2938977, 8462447, 24366645, 70160958, 202020427, 581694636, 1674922950, 4822748423, 13886550633, 39984728949, 115131438424, 331507764639
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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REFERENCES
| Martin H. Gutknecht and Lloyd N. Trefethen, Real Polynomial Chebyshev Approximation by the Caratheodory-Fejer Method.
Rosenblum and Rovnyak, Hardy Classes and Operator Theory, Dover, New York, 1985, page 26
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FORMULA
| a(n)=3a(n-1)-a(n-3), a(0)=0, a(1)=1, a(2)=3 (follows from the minimal polynomial x^3-3x^2+1 of the matrix M).
a(n)=A076264(n-1). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jun 18 2008
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MAPLE
| with(linalg): M[1]:=matrix(3, 3, [2, 1, 1, 1, 1, 0, 1, 0, 0]): for n from 2 to 26 do M[n]:=multiply(M[1], M[n-1]) od: 0, seq(M[n][1, 2], n=1..26);
a[0]:=0: a[1]:=1: a[2]:=3: for n from 3 to 26 do a[n]:=3*a[n-1]-a[n-3] od: seq(a[n], n=0..26);
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MATHEMATICA
| M = {{2, 1, 1}, {1, 1, 0}, {1, 0, 0}}; v[1] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a2 = Table[v[n][[2]], {n, 1, 50}]
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CROSSREFS
| Cf. A122099, A122100.
Sequence in context: A171277 A000243 A076264 * A018919 A005774 A101169
Adjacent sequences: A123938 A123939 A123940 * A123942 A123943 A123944
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KEYWORD
| nonn
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AUTHOR
| Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Oct 25 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 07 2006
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