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Search: id:A152060
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| A152060 |
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Triangle read by rows, characteristic polynomials of Cartan ring matrices. |
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+0
1
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| 1, 1, -2, 1, -4, 3, 1, -6, 9, -4, 1, -8, 20, -16, 4, 1, -10, 35, -50, 25, -4, 1, -12, 54, -112, 105, -36, 4, 1, -14, 77, -210, 294, -196, 49, -4, 8, -16, 104, -352, 660, -672, -64, 4, 9, -18, 135, -546, 1287, -1782, 1386, -540, 81, -4, 1, -20, 170, -800, 2275, -4004, 4290
(list; table; graph; listen)
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OFFSET
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0,3
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REFERENCES
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William G. Harter, University of Arkansas; personal communication
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FORMULA
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Triangle read by rows, n-th row = characteristic polynomial of n X n Cartan ring matrix, defined as a Cartan matrix with 1's in the upper right and lower left corners, i.e. positions (1,n) and (n,1).
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EXAMPLE
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First few rows of the triangle =
1;
1, -2;
1, -4, 3;
1, -6, 9, -4;
1, -8, 20, -16, 4;
1, -10, 35, -50, 25, -4;
1, -12, 54, -112, 105, -36, 4;
1, -14, 77, -210, 294, -196, 49, -4;
1, -16, 104, -352, 660, -672, 64, -64, 4;
1, -18, 135, -546, 1287, -1782, 1386, -540, 81, -4;
1, -20, 170, -800, 2275, -4004, 4290, 2640, 825, -100, 4;
...
Example: 5-th degree = x^5 -10x^4 + 35x^3 -50x^2 + 25x - 4,
factorable into (x - 4) * (x^2 - 3x + 1)^2
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CROSSREFS
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Sequence in context: A093966 A103406 A142978 this_sequence A093190 A132191 A094437
Adjacent sequences: A152057 A152058 A152059 this_sequence A152061 A152062 A152063
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KEYWORD
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tabl,sign
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AUTHOR
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Gary W. Adamson & Roger L. Bagula (qntmpkt(AT)yahoo.com), Nov 22 2008
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