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Search: id:A107248
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| A107248 |
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First entry of the vector (M^n)v, where M is the 6x6 matrix [[0,1,0,0,0,0],[0,0,1,0,0,0],[0,2,0,5,0,0],[0,0,0,0,1,0],[0,0,0,0,0,1],[5,0,0,0,2,0]] and v is the column vector [[1,1,1,7,7,19]. |
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10
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| 1, 1, 1, 37, 37, 169, 169, 553, 553, 2461, 2461, 11857, 11857, 51409, 51409, 219733, 219733, 969721, 969721, 4285177, 4285177, 18755149, 18755149, 82122913, 82122913, 360600481, 360600481, 1582788997, 1582788997, 6941826889
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OFFSET
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0,4
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COMMENT
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Characteristic polynomial of the matrix M is (x^3-2x+5)(x^3-2x-5).
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MAPLE
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with(linalg): M:=matrix(6, 6, [0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 5, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 1, 5, 0, 0, 0, 2, 0]): v[0]:=matrix(6, 1, [1, 1, 1, 7, 7, 19]): for n from 1 to 35 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..35): seq(v[n][1, 1], n=0..35);
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MATHEMATICA
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M = {{0, 1, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0}, {0, 2, 0, 5, 0, 0}, {0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 1}, {5, 0, 0, 0, 2, 0}} v[1] = {1, 1, 1, 7, 7, 19} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}] Det[M - x*IdentityMatrix[6]]
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CROSSREFS
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Cf. A007493.
Sequence in context: A022993 A023479 A090179 this_sequence A043611 A071887 A111043
Adjacent sequences: A107245 A107246 A107247 this_sequence A107249 A107250 A107251
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 08 2005
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EXTENSIONS
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Edited by njas, May 13 2006
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