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Search: id:A124040
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| A124040 |
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3 center "cycle" matrices as a triangular sequence based on the triagular model: m(n,m,3)={{3, 1, 1}, {1, 3, 1}, {1, 1, 3}} m(n,m,d)=If[ n == m, 3, If[n == m - 1 || n ==m + 1, 1, If[(n == 1 && m == d) || (n == d && m == 1), 1, 0]]]. |
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| 3, 3, -1, 8, -6, 1, 20, -24, 9, -1, 45, -84, 50, -12, 1, 125, -275, 225, -85, 15, -1, 320, -864, 900, -468, 129, -18, 1, 845, -2639, 3339, -2219, 840, -182, 21, -1, 2205, -7896, 11756, -9528, 4610, -1368, 244, -24, 1, 5780, -23256, 39825, -38121, 22518, -8532, 2079, -315, 27, -1, 15125, -67650, 130975
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Matrices: 1 X 1 {{3}}, 2 X 2 {{3, 1}, {1, 3}}, 3 X 3 {{3, 1,1}, {1, 3, 1}, {1, 1, 3}}, 4 X 4 {{3, 1, 0, 1}, {1, 3, 1, 0}, {0, 1, 3, 1}, {1, 0, 1, 3}}, 5 X 5 {{3, 1, 0, 0, 1}, {1, 3, 1, 0, 0}, {0, 1, 3, 1, 0}, {0, 0, 1, 3, 1}, {1, 0, 0, 1, 3}} Large Root: Table[x /. NSolve[Det[M[d] - x*IdentityMatrix[d]] == 0, x][[d]], {d, 1, 10}] {3., 4., 5., 5., 5., 5., 5., 5., 5., 5.}
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FORMULA
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m(n,m,d)=If[ n == m, 3, If[n == m - 1 || n ==m + 1, 1, If[(n == 1 && m == d) || (n == d && m == 1), 1, 0]]]
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EXAMPLE
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Triangle begins:
{3},
{3, -1},
{8, -6, 1},
{20, -24, 9, -1},
{45, -84, 50, -12, 1},
{125, -275,225, -85, 15, -1}
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MATHEMATICA
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T[n_, m_, d_] := If[ n == m, 3, If[n == m - 1 || n == m + 1, 1, If[(n == 1 && m == d) || (n == d && m == 1), 1, 0]]] M[d_] := Table[T[n, m, d], {n, 1, d}, {m, 1, d}] Table[M[d], {d, 1, 10}] Table[Det[M[d]], {d, 1, 10}] Table[Det[M[d] - x*IdentityMatrix[d]], {d, 1, 10}] a = Join[M[1], Table[CoefficientList[Det[M[d] - x*IdentityMatrix[d]], x], {d, 1, 10}]] Flatten[a] MatrixForm[a]
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CROSSREFS
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Sequence in context: A079268 A102316 A133709 this_sequence A078033 A108075 A084145
Adjacent sequences: A124037 A124038 A124039 this_sequence A124041 A124042 A124043
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KEYWORD
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uned,probation,tabl,sign
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AUTHOR
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Gary Adamson and Roger Bagula (rlbagulatftn(AT)yahoo.com), Nov 04 2006
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