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Search: id:A115605
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| A115605 |
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Dihedral D3 elliptical invariant transform on A000045: a[n+1]/a[n]= Phi^3=((1+Sqrt[5])/2)^3. |
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+0
1
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| 0, 0, 2, 7, 31, 128, 549, 2315, 9826, 41594, 176242, 746496, 3162334, 13395658, 56745250, 240376201, 1018250793, 4313378176, 18271765435, 77400436781, 327873517634, 1388894499108, 5883451527348, 24922700587008
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OFFSET
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0,3
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COMMENT
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A D3 elliptical invariant transform gives a ratio of Phi^3. Ratios from the Dihedral transforms are: D1->Phi D2->1+Phi D3->Phi^3
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FORMULA
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b[n]=A000045[n] g[x]=(x^3-1)^2/(-4*x^3): D3 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^3 - 1)^2/(-4*x^3) 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: A102162 A059846 A034698 this_sequence A114198 A055836 A076177
Adjacent sequences: A115602 A115603 A115604 this_sequence A115606 A115607 A115608
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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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