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Search: id:A115348
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| A115348 |
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Five coordinate renormalization of A5 to pentadentate D2 polynomial as a coeffiecient expansion. |
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+0
1
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| 16384, 327680, 3440640, 12107776, 25231360, 242155520, 145080320, 2542632960, 3921969152, 18645975040, 67413278720, 107214356480, 688149954560, 882910511104, 5003772477440, 9509919129600, 28675705569280, 85303631052800
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OFFSET
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0,1
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COMMENT
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The idea of this renormalization is a symmetry collapse/ catastrophe in the sense of Thom in which a higher A5 symmetery dodecahedron collapses in renormalization to a very simple D2 at an order of 10 degeneracies.
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REFERENCES
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Elliptical invariants taken from: Jones and Singerman, Belyi Functions, Hypermaps and Galois Groups, Bull. London Math. Soc.,28 (1996) pp. 561-590: page 585
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FORMULA
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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)
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MATHEMATICA
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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]}]]
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CROSSREFS
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Sequence in context: A069389 A069415 A069275 this_sequence A016783 A016807 A016903
Adjacent sequences: A115345 A115346 A115347 this_sequence A115349 A115350 A115351
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KEYWORD
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nonn,uned
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AUTHOR
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Roger Bagula (rlbagulatftn(AT)yahoo.com), Mar 07 2006
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