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Search: id:A136705
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| A136705 |
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Triangular sequence of coefficients of characteristic polynomials for Fibonacci-type matrix for a=1; b=1: example: M(4)= {{0, 0, 0, 1}, {1, 0, 0, 0}, {0, 1, 0, 0}, {0, 0, 1, 1}}. |
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+0
1
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| 1, 1, -1, -1, -1, 1, 1, 0, 1, -1, -1, 0, 0, -1, 1, 1, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, -1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 1, -1, -1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Row sums are:
{1, 0, -1, 1, -1, 1, -1, 1, -1, 1, -1};
If these are vector reversed and the absolute value taken, they are the same as the Galois field triangular sequence.
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REFERENCES
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J. Cigler, q-Fibonacci polynomials, Fibonacci Quarterly, 2003; http://homepage.univie.ac.at/johann.cigler/downloads/FIBQUART.pdf
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FORMULA
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t(n,m,d)=If[ n == m == d, 1, If[m == d && n == 1, 1, If[n == m + 1, 1, 0]]]
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EXAMPLE
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{1},
{1, -1},
{-1, -1, 1},
{1, 0, 1, -1},
{-1, 0, 0, -1, 1},
{1, 0, 0, 0, 1, -1},
{-1, 0, 0, 0, 0, -1, 1},
{1, 0, 0, 0, 0, 0, 1, -1},
{-1, 0, 0, 0, 0, 0, 0, -1, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 1, -1},
{-1, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1}
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MATHEMATICA
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T[n_, m_, d_] := If[ n == m == d, 1, If[m == d && n == 1, 1, If[n == m + 1, 1, 0]]]; M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}]; Table[Det[M[d]], {d, 1, 10}]; Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}]; a = Join[{{1}}, Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]]; Flatten[a]
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CROSSREFS
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Adjacent sequences: A136702 A136703 A136704 this_sequence A136706 A136707 A136708
Sequence in context: A117947 A092152 A075743 this_sequence A141646 A129573 A118172
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KEYWORD
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uned,tabl,easy,more,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 06 2008
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