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Search: id:A122766
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| A122766 |
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Triangle read by rows, based on the coefficients of the second derivatives of the polynomials in A122601. Let p(k, x) = x*p(k - 1, x) - p(k - 2, x). Then T(k,x)=d^2 p(k,x)/dx^2. |
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+0
2
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| 2, -2, 6, -6, -6, 12, 6, -24, -12, 20, 12, 24, -60, -20, 30, -12, 60, 60, -120, -30, 42, -20, -60, 180, 120, -210, -42, 56, 20, -120, -180, 420, 210, -336, -56, 72
(list; table; graph; listen)
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OFFSET
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1,1
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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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2
-2, 6
-6, 6, 12
6, -24, -12, 20
12, 24, -60, -20, 30
12, 60, 60, -120,-30, 42
-20, -60, 180, 120,-210, -42, 56
20,-120, -180, 420, 210,-336, -56, 72
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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, 2}], x], {n, 2, 10}]; Flatten[w1]
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CROSSREFS
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Cf. A122601, A066170, A046854.
Sequence in context: A140219 A077081 A084700 this_sequence A033742 A048594 A130493
Adjacent sequences: A122763 A122764 A122765 this_sequence A122767 A122768 A122769
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KEYWORD
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sign,more,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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EXTENSIONS
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Edited by N. J. A. Sloane (njas(AT)research.att.com), Oct 01 2006
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