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Search: id:A147663
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| A147663 |
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Coefficient expansion of toral of inverse of low ratio (1.3247179572447476) Salem Polynomial: a(n)=Coefficient_Expansion(1/(-1 + x^2 - x^4 + x^8 - x^9 - x^10 + x^11)). |
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+0
1
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| 1, 1, 2, 2, 3, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 50, 66, 88, 116, 154, 203, 269, 356, 472, 625, 828, 1097, 1453, 1925, 2550, 3379, 4476, 5930, 7855, 10406, 13784, 18260, 24189, 32044, 42449, 56233, 74493, 98682, 130726, 173175, 229409, 303902, 402585
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Minimal Pisot (Padovan) factor: Factor[ -1 + x^2 - x^4 + x^8 - x^9 - x^10 + x^11]= (-1 - x + x^3)*(1 - x + x^3 - x^4 + x^5 - x^7 + x^8). Census that produced this polynomial took two hours to run in Mathematica. The ratio of McMullen's Salem is higher at:1.3728862806447408
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REFERENCES
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Curtis T. McMullen,Dynamics on K3 surfaces: Salem numbers and Siegel disks,2005, http://abel.math.harvard.edu/~ctm/papers/index.html
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FORMULA
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a(n)=Coefficient_Expansion(1/(-1 + x^2 - x^4 + x^8 - x^9 - x^10 + x^11)).
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MATHEMATICA
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f[x_] = -1 + x^2 - x^4 + x^8 - x^9 - x^10 + x^11; g[x] = ExpandAll[x^11*f[1/x]]; a = Table[SeriesCoefficient[Series[1/g[x], {x, 0, 50}], n], {n, 0, 50}]
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CROSSREFS
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A143478, A143419
Sequence in context: A018243 A113788 A127207 this_sequence A089047 A036811 A059185
Adjacent sequences: A147660 A147661 A147662 this_sequence A147664 A147665 A147666
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KEYWORD
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nonn
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AUTHOR
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Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Nov 09 2008
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