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Search: id:A123185
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| A123185 |
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Triangular array from a zero coefficient sum of recursive polynomials: p(k, x) = x*p(k - 1, x) + p(k - 2, x). |
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+0
1
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| -1, -1, 1, 2, -3, 1, -1, 3, -3, 1, 2, -4, 4, -3, 1, -1, 5, -7, 5, -3, 1, 2, -5, 9, -10, 6, -3, 1, -1, 7, -12, 14, -13, 7, -3, 1, 2, -6, 16, -22, 20, -16, 8, -3, 1, -1, 9, -18, 30, -35, 27, -19, 9, -3, 1, 2, -7, 25, -40, 50, -51, 35, -22, 10, -3, 1
(list; table; graph; listen)
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OFFSET
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1,4
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COMMENT
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Except fpr p(0,x)=1 all sum to zero: Table[Sum[CoefficientList[p[n, x], x][[m]], {m, 1, n + 1}], {n, 0, 12}] {1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0}
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FORMULA
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p(k, x) = x*p(k - 1, x) + p(k - 2, x)
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EXAMPLE
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1
-1, 1
2, -3, 1
-1, 3, -3, 1
2, -4, 4, -3, 1
-1, 5, -7, 5, -3, 1
2, -5, 9, -10, 6, -3, 1
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MATHEMATICA
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p[0, x] = 1; p[1, x] = x - 1; p[2, x] = x^2 - 3x + 2; p[k_, x_] := p[k, x] = x*p[k - 1, x] + p[k - 2, x] ; w = Table[CoefficientList[p[n, x], x], {n, 0, 10}]; Flatten[w]
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CROSSREFS
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Sequence in context: A054722 A067627 A077233 this_sequence A133569 A141071 A004648
Adjacent sequences: A123182 A123183 A123184 this_sequence A123186 A123187 A123188
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KEYWORD
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tabl,uned,sign
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Oct 02 2006
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