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A127694
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Absolute value of coefficient of x^3 in polynomial whose zeros are 5 consecutive integers starting with the n-th integer.
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1
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580, 1175, 2070, 3325, 5000, 7155, 9850, 13145, 17100, 21775, 27230, 33525, 40720, 48875, 58050, 68305, 79700, 92295, 106150, 121325, 137880, 155875, 175370, 196425, 219100, 243455, 269550, 297445, 327200, 358875, 392530, 428225, 466020
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| Sums of all distinct products of 3 out of 5 consecutive integers, starting with the n-th integer; value of 3rd elementary symmetric function on the 5 consecutive integers. cf. Vieta's formulas.
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MATHEMATICA
| r = {}; k = 0; a = {}; Do[Do[Do[If[(d != b) && (d != c) && (b != c), AppendTo[a, {d, b, c}]], {c, b, 5}], {b, d, 5}], {d, 1, 5}]; Do[Do[k = k + Sum[(x + a[[v, 1]]) (x + a[[v, 2]]) (x + a[[v, 3]]), {v, 1, Length[a]}]]; AppendTo[r, k]; k = 0, {x, 1, 50}]; r
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CROSSREFS
| Cf. A127694, A127350.
Sequence in context: A097769 A186786 A185609 * A185605 A186784 A185606
Adjacent sequences: A127691 A127692 A127693 * A127695 A127696 A127697
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KEYWORD
| nonn
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AUTHOR
| Artur Jasinski (grafix(AT)csl.pl), Jan 23 2007
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