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Search: id:A115852
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| A115852 |
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Dihedral D3 elliptical invariant transform on A000045: a[n+1]/a[n]= Phi^4=((1+Sqrt[5])/2)^4. |
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+0
1
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| 0, 0, 4, 20, 156, 1024, 7140, 48620, 334084, 2287656, 15685560, 107495424, 736823880, 5050163160, 34614602500, 237251310140, 1626146516820, 11145769206784, 76394251284780, 523613954825156, 3588903524021764
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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A D4 elliptical invariant transform gives a ratio of Phi^4. Ratios from the Dihedral transforms are: D1->Phi D2->1+Phi=Phi^2 D3->Phi^3 D4->Phi^4
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FORMULA
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b[n]=A000045[n] g[x]=(x^4-1)^2/(-4*x^4): D4 dihedral elliptical invariant function a(n) = -Floor[g[b[n]]
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MATHEMATICA
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F[0] = 0; F[1] = 1; F[n_] := F[n] = F[n - 1] + F[n - 2] g[x_] = (x^4 - 1)^2/(-4*x^4) a = Table[ -Floor[g[F[n]]], {n, 1, 25}] Table[N[a[[n + 1]]/a[[n]]], {n, 1, Length[a] - 1}]
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CROSSREFS
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Cf. A000045, A079962.
Sequence in context: A094070 A119022 A006682 this_sequence A058381 A094651 A065526
Adjacent sequences: A115849 A115850 A115851 this_sequence A115853 A115854 A115855
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KEYWORD
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nonn,probation
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Mar 13 2006
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