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Search: id:A122188
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| A122188 |
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Triangle read by rows, formed from the coefficients of characteristic polynomials of the following sequence of matrices: 2 X 2 {{0, 1}, {1, 1}}, 3 X 3 {{0, 1, 0}, {0, 0, 1}, {1, 1, 1}}, 4 X 4 {{0, 1,0, 0}, {0, 0, 1, 0}, {0, 0, 0, 1}, {1, 1, 1, 1}}, 5 X 5 {{0, 1, 0, 0, 0}, {0, 0, 1, 0, 0}, {0, 0, 0, 1, 0}, {0, 0, 0, 0, 1}, {1, 1, 1, 1, 1}}, ... |
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+0
3
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| 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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, 2, -3, 4, -5, 6, -7, 8, -9}
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FORMULA
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B(x, n) = If[n > 1, (-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}])]
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EXAMPLE
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Triangular array:
{1},
{1, -1},
{-1, -1, 1},
{1, 1, 1, -1},
{-1, -1, -1, -1, 1},
{1, 1, 1,1, 1, -1},
{-1, -1, -1, -1, -1, -1,1},
{1, 1, 1, 1, 1, 1, 1, -1},
{-1, -1, -1, -1, -1, -1, -1, -1, 1}
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MATHEMATICA
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An[d_] := Table[If[n == d, 1, If[m == n + 1, 1, 0]], {n, 1, d}, {m, 1, d}]; Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[An[d], x], x], {d, 1, 20}]]; Flatten[%]
Clear[B, x, n] B[x, 0] = 1; B[x, 1] = -x + 1; B[x_, n_] := B[x, n] = If[n > 1, (-1)^n*(x^n - Sum[x^m, {m, 0, n - 1}])]; Table[ExpandAll[B[x, n]], {n, 0, 10}]; a = Table[CoefficientList[B[x, n], x], {n, 0, 10}]; Flatten[a] Table[Apply[Plus, CoefficientList[B[x, n], x]], {n, 0, 10}]
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CROSSREFS
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Cf. A000073, A000045.
Sequence in context: A106400 A112865 A121241 this_sequence A130151 A131561 A065357
Adjacent sequences: A122185 A122186 A122187 this_sequence A122189 A122190 A122191
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KEYWORD
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tabl,sign
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AUTHOR
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Gary Adamson and Roger Bagula (qntmpkt(AT)yahoo.com), Oct 18 2006, Mar 18 2008
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EXTENSIONS
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Edited by njas, Apr 14 2008
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