A115348 Five-coordinate renormalization of A_5 to pentadentate D_2 polynomial as a coefficient expansion.

16384, 327680, 3440640, 12107776, 25231360, 242155520, 145080320, 2542632960, 3921969152, 18645975040, 67413278720, 107214356480, 688149954560, 882910511104, 5003772477440, 9509919129600, 28675705569280, 85303631052800

Offset

0,1

Comments

The idea of this renormalization is a symmetry collapse/ catastrophe in the sense of Thom in which a higher A_5 symmetry dodecahedron collapses in renormalization to a very simple D2 at an order of 10 degeneracies.

Links

Table of n, a(n) for n=0..17.

Gareth Jones and David Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc., 28 (1996), 561-590. See p. 585.

Formula

a(n) = 27*coefficient expansion of -16384*x^15*(x^20 - 228* x^15 + 494*x^10 + 228*x^5 + 1)^3/(27*(-1 + x^2)^20*(x^10 + 11*x^5 - 1)^5)

Mathematica

jA5[x_] = (x^20 - 228*x^15 + 494*x^10 + 228*x^5 + 1)^3/(-1728*x^5*(x^10 + 11* x^5 - 1)^5) jD2[x_] = (x^2 - 1)^2/(-4*x^2) p[x_]=FullSimplify[jA5[x]/jD2[x]^10] a = Flatten[27*{{p[0]}, Table[Coefficient[Series[p[x], {x, 0, 45}], x^n], {n, 1, 45}]}] aout = Flatten[Table[If[a[[n]] == 0, {}, a[[n]]], {n, 1, Length[a]}]]

Crossrefs

Sequence in context: A258736 A255666 A220767 * A218528 A016783 A016807

Adjacent sequences: A115345 A115346 A115347 * A115349 A115350 A115351

Keyword

nonn,uned

Author

Roger L. Bagula, Mar 07 2006

Status

approved