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Search: id:A113279
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| A113279 |
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Triangle T(n,k) of coefficients of r_1^n+r_2^n in terms of p and q, where r_1,r_2 are the roots of x^2+px+q=0. |
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1
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| 2, -1, 1, -2, -1, 3, 1, -4, 2, -1, 5, -5, 1, -6, 9, -2, -1, 7, -14, 7, 1, -8, 20, -16, 2, -1, 9, -27, 30, -9, 1, -10, 35, -50, 25, -2, -1, 11, -44, 77, -55, 11, 1, -12, 54, -112, 105, -36, 2, -1, 13, -65, 156, -182, 91, -13, 1, -14, 77, -210, 294, -196, 49, -2, -1, 15, -90, 275, -450, 378, -140, 15
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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The triangle begins: 2 .-1 1..-2 .-1..3 1..-4.2
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REFERENCES
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M. Herkenhoff Konersmann, Sprokkel XXXI: x_1^n+x_2^n, Nieuw Tijdschr. Wisk, 42 (1954-55) 180.
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FORMULA
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T(n, k)=(-1)^(n+k)*A034807(n, k)
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EXAMPLE
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x_1^5+x_2^5 = -p^5 + 5p^3q - 5pq^2, so row 5 reads -1, 5, -5.
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CROSSREFS
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Sequence in context: A127586 A055893 A050221 this_sequence A034807 A135062 A088428
Adjacent sequences: A113276 A113277 A113278 this_sequence A113280 A113281 A113282
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KEYWORD
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easy,sign,tabf
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AUTHOR
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Floor van Lamoen (fvlamoen(AT)hotmail.com), Oct 22 2005
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