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A113976
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a(n)= 4*a(n-1) -3*a(n-2), n>4.
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0
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14, 133, 616, 2128, 6664, 20272, 61096, 183568, 550984, 1653232, 4959976, 14880208, 44640904, 133922992, 401769256, 1205308048, 3615924424, 10847773552, 32543320936, 97629963088, 292889889544, 878669668912
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| I was trying to get an integer root cubic over cubic that had the Farey conditions: p[1/2]=1;p[0]=0;p[1]=0
The function has the characteristic Farey shape: fa[x_] := 1/p[x] /; 0 <= x <= 1/2 fa[x_] := p[x] /; 1/2 < x <= 1
My theory was that there should be a family of Farey type functions of the form: p[x]=k*(x - a)*(x - b)*(x -c)/((x - d)*(x - e)*(x - f))
with integer root ( rational) structure ( simply starting at abc=123): Abs[a*b*c]=Abs[d*f] and sign[a*b*c]=Sign[d*f]; e=0
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FORMULA
| G.f.: 7*(2+3*x)*(3*x+1)*(1+x)/((3*x-1)*(x-1)) [Sep 28 2009]
a(n) = 84*3^n-140, n>1. [Sep 28 2009]
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MATHEMATICA
| a = 1; b = 2; c = 3; d = -3; e = 0; f = -1; p[x_] = FullSimplify[ExpandAll[(-7/ 5)*(x - a)*(x - b)*(x -c)/((x - d)*(x - e)*(x - f))]] a = Abs[ReplacePart[Table[5*Coefficient[Series[p[x] , {x, 0, 30}], x^n]*3^(n + 1), {n, -1, 30}], -133, 2]]
Join[{14, 133}, LinearRecurrence[{4, -3}, {616, 2128}, 20]] (* From Harvey P. Dale, Nov 14 2011 *)
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CROSSREFS
| Cf. A113923.
Sequence in context: A206207 A026936 A021114 * A022738 A017269 A021079
Adjacent sequences: A113973 A113974 A113975 * A113977 A113978 A113979
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KEYWORD
| nonn,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Jan 31 2006
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EXTENSIONS
| Definition replaced by recurrence by the Associate Editors of the OEIS, Sep 28 2009
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