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Search: id:A122765
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| A122765 |
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Triangle read by rows, based on the coefficients of derivatives of the polynomials in A122601. Let p(k, x) = x*p(k - 1, x) - p(k - 2, x). Then T(k,x)=dp(k,x)/dx |
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+0
2
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| 1, -1, 2, -2, -2, 3, 2, -6, -3, 4, 3, 6, -12, -4, 5, -3, 12, 12, -20, -5, 6, -4, -12, 30, 20, -30, -6, 7, 4, -20, -30, 60, 30, -42, -7, 8, 5, 20, -60, -60, 105, 42, -56, -8, 9
(list; table; graph; listen)
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OFFSET
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1,3
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REFERENCES
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P. Steinbach, Golden fields: a case for the heptagon, Math. Mag. 70 (1997), no. 1, 22-31.
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EXAMPLE
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1
-1, 2
-2,-2, 3
2, -6,-3, 4
3, 6, -12, -4, 5
-3, 12, 12,-20,-5, 6
-4, -12, 30, 20, -30, -6, 7
4, -20, -30, 60, 30, -42, -7, 8
5, 20, -60, -60, 105, 42, -56, -8, 9
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MATHEMATICA
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p[0, x] = 1; p[1, x] = x - 1; p[k_, x_] := p[k, x] = x*p[k - 1, x] - p[k - 2, x]; a = Table[Expand[p[n, x]], {n, 0, 10}]; w1 = Table[CoefficientList[D[a[[n]], x], x], {n, 2, 10}]; Flatten[w1]
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CROSSREFS
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Cf. A122601, A066170, A046854, A122766.
Sequence in context: A058614 A058726 A132321 this_sequence A131053 A125600 A084053
Adjacent sequences: A122762 A122763 A122764 this_sequence A122766 A122767 A122768
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KEYWORD
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sign,tabl
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AUTHOR
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Roger Bagula and Gary Adamson (rlbagulatftn(AT)yahoo.com), Sep 22 2006
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