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 A135645 Polynomial expansion of p(x)=(-17 - 98 x^9 + x^10)(-1 - 2 x^9 + x^10)^3(-1 - x^9 + x^10)^6 as: 1/(p(1/x)*x^100). 0
 1, 110, 10861, 1064784, 104350518, 10226356908, 1002182997326, 98213933800552, 9624965512636055, 943246620238838634, 92438168783407537949, 9058940540773942228850, 887776172995846347486624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Matrix polynomial of three level 10by10 10 person game as 100by100 Matrix Markov. LINKS FORMULA p(x)=(-17 - 98 x^9 + x^10)(-1 - 2 x^9 + x^10)^3(-1\) - x^9 + x^10)^6 a(n) = expansion of(1/(p(1/x)*x^100)) MATHEMATICA f[x_] = Product[CharacteristicPolynomial[{{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 0, 0, 0, 0, 0, a}}, x]^(6/a), {a, 1, 2}]*CharacteristicPolynomial[{{0, 1, 0, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 1, 0, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 1, 0, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 1, 0, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 1, 0, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 1, 0, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 1, 0, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 1, 0}, {0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {17, 0, 0, 0, 0, 0, 0, 0, 0, 98}}, x]; g[x_] = Expand[x^100*f[1/x]]; a = Table[ SeriesCoefficient[Series[1/g[x], {x, 0, 30}], n], {n, 0, 30}] CROSSREFS Sequence in context: A266844 A265319 A267854 * A266299 A265696 A267535 Adjacent sequences:  A135642 A135643 A135644 * A135646 A135647 A135648 KEYWORD nonn,uned AUTHOR Roger L. Bagula, Jan 31 2008 STATUS approved

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)