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Search: id:A122788
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| A122788 |
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(1,3)-entry of the 3 X 3 matrix M^n, where M={{0, -1, 1}, {1, 1, 0}, {0, 1, 1}}. |
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+0
1
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| 0, 1, 1, 0, 0, 2, 4, 4, 4, 8, 16, 24, 32, 48, 80, 128, 192, 288, 448, 704, 1088, 1664, 2560, 3968, 6144, 9472, 14592, 22528, 34816, 53760, 82944, 128000, 197632, 305152, 471040, 727040, 1122304, 1732608, 2674688, 4128768, 6373376, 9838592, 15187968
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OFFSET
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0,6
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FORMULA
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Rec. rel: a(n)=2a(n-1)-2a(n-2)+2a(n-3) (follows from the minimal polynomial of the matrix M).
a(n)=A078003(n-1). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 02 2008]
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EXAMPLE
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a(7)=4 because M^7 ={{0,4,4},{4,4,8},{8,12,12}}.
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MAPLE
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with(linalg): M[1]:=matrix(3, 3, [0, -1, 1, 1, 1, 0, 0, 1, 1]): for n from 2 to 42 do M[n]:=multiply(M[1], M[n-1]) od: 0, seq(M[n][1, 3], n=1..42);
a[0]:=0: a[1]:=1: a[2]:=1: for n from 3 to 42 do a[n]:=2*a[n-1]-2*a[n-2]+2*a[n-3] od: seq(a[n], n=0..42);
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MATHEMATICA
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M = {{0, -1, 1}, {1, 1, 0}, {0, 1, 1}}; v[1] = {0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
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Sequence in context: A076345 A160809 A139251 this_sequence A078003 A081524 A021413
Adjacent sequences: A122785 A122786 A122787 this_sequence A122789 A122790 A122791
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KEYWORD
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nonn
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 20 2006
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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Nov 24 2006
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