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Search: id:A136451
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| A136451 |
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An anti-diagonal version of the Cartan A_n group matrix: Characteristic polynomials as coefficient triangle ( a tri-anti-diagonal matrix): example n=3: {{0, -1, 2}, {-1, 2, -1}, {2, -1, 0}}. |
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+0
1
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| 1, 2, -1, -3, 2, 1, -4, 6, 2, -1, 5, -10, -9, 2, 1, 6, -19, -16, 12, 2, -1, -7, 28, 42, -22, -15, 2, 1, -8, 44, 68, -74, -28, 18, 2, -1, 9, -60, -138, 126, 115, -34, -21, 2, 1, 10, -85, -208, 316, 202, -165, -40, 24, 2, -1, -11, 110, 363, -506, -605, 296, 224, -46, -27, 2, 1
(list; table; graph; listen)
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OFFSET
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1,2
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COMMENT
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Row sums are:
{1, 1, 0, 3, -11, -16, 29, 21, 0, 55, -199}
Is this (apart from the first term) the same as A124018? - R. J. Mathar (mathar(AT)strw.leidenuniv.nl) Apr 29 2008
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FORMULA
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h(i,j)=If[i + j - 1 == n, 2, If[i + j - 1 == n + 1, -1, If[i + j - 1 == n - 1, -1, 0]]]; i,j<=n
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EXAMPLE
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{1},
{2, -1},
{-3,2, 1},
{-4, 6, 2, -1},
{5, -10, -9, 2, 1},
{6, -19, -16, 12, 2, -1},
{-7,28, 42, -22, -15, 2, 1},
{-8, 44, 68, -74, -28,18, 2, -1},
{9, -60, -138, 126, 115, -34, -21, 2, 1},
{10, -85, -208,316, 202, -165, -40, 24, 2, -1},
{-11, 110, 363, -506, -605, 296, 224, -46, -27, 2, 1}
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MATHEMATICA
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H[n_] := Table[Table[If[i + j - 1 == n, 2, If[i + j - 1 == n + 1, -1, If[i + j - 1 == n - 1, -1, 0]]], {i, 1, n}], {j, 1, n}]; a = Join[{{1}}, Table[CoefficientList[CharacteristicPolynomial[H[n], x], x], {n, 1, 10}]]; Flatten[a']
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CROSSREFS
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Adjacent sequences: A136448 A136449 A136450 this_sequence A136452 A136453 A136454
Sequence in context: A029635 A104741 A089353 this_sequence A066121 A039911 A002335
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KEYWORD
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uned,tabl,sign
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 19 2008
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