A115852 Dihedral D3 elliptical invariant transform on A000045: a[n+1]/a[n]= Phi^4=((1+Sqrt[5])/2)^4.

0, 0, 4, 20, 156, 1024, 7140, 48620, 334084, 2287656, 15685560, 107495424, 736823880, 5050163160, 34614602500, 237251310140, 1626146516820, 11145769206784, 76394251284780, 523613954825156, 3588903524021764

Offset: 0

Author

Roger L. Bagula, Mar 13 2006

Keywords

• nonn
• uned

Comments

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

Crossrefs

Cf. A000045, A079962.

Programs

Mathematica

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}]

Formula

b[n]=A000045[n] g[x]=(x^4-1)^2/(-4*x^4): D4 dihedral elliptical invariant function a(n) = -Floor[g[b[n]]