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A122822
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The (1,4) entry in the matrix M^n, where M is the 4 X 4 matrix [[0,-1,1,0],[0,0,-1,1],[1,1,1,0],[0,1,1,1]] (n>=0).
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0
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0, 0, -1, 0, 0, -1, 1, 2, 3, 10, 19, 35, 71, 131, 240, 446, 810, 1467, 2660, 4792, 8621, 15501, 27814, 49873, 89384, 160079, 286589, 512943, 917813, 1641978, 2937132, 5253248, 9395035, 16801268, 30044388, 53724067, 96064297, 171769178, 307129259, 549150614, 981877515, 1755576755, 3138916347
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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FORMULA
| a(n)=2a(n-1)+a(n-3)-3a(n-4) for n>=4; a(0)=0, a(1)=-1, a(2)=0, a(3)=0.
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MAPLE
| a[0]:=0: a[1]:=0: a[2]:=-1: a[3]:=0: for n from 4 to 42 do a[n]:=2*a[n-1]+a[n-3]-3*a[n-4] od: seq(a[n], n=0..42);
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MATHEMATICA
| M = {{0, -1, 1, 0}, {0, 0, -1, 1}, {1, 1, 1, 0}, {0, 1, 1, 1}}; v[1] = {0, 0, 0, 1}; v[n_] := v[n] = M.v[n - 1]; a1 = Table[v[n][[1]], {n, 1, 50}]
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CROSSREFS
| Sequence in context: A143045 A156909 A175569 * A083944 A165550 A184261
Adjacent sequences: A122819 A122820 A122821 * A122823 A122824 A122825
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KEYWORD
| sign
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AUTHOR
| Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 20 2006
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 26 2006
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