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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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9
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Characteristic polynomial of the matrix M is (x^3-2x+5)(x^3-2x-5).
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FORMULA
| G.f.: -(1+x-3*x^2+33*x^3+37*x^4+25*x^5)/((5*x^3-2*x^2+1)*(5*x^3+2*x^2-1)). a(n)= 4*a(n-2)-4*a(n-4)+25*a(n-6). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 03 2009]
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MAPLE
| 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
| 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
| Cf. A007493.
Sequence in context: A022993 A023479 A090179 * A165858 A190839 A185698
Adjacent sequences: A107245 A107246 A107247 * A107249 A107250 A107251
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KEYWORD
| nonn
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jun 08 2005
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EXTENSIONS
| Edited by N. J. A. Sloane (njas(AT)research.att.com), May 13 2006
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