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Search: id:A083024
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| A083024 |
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Molien series for action of SL(3,C) on ternary forms of degree 4. |
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1
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| 1, 1, 2, 4, 7, 11, 19, 29, 44, 67, 98, 139, 199, 275, 375, 509, 678, 890, 1165, 1501, 1916, 2431, 3053, 3801, 4711, 5788, 7063, 8580, 10353, 12420, 14841, 17633, 20850, 24565, 28807, 33641, 39161, 45404, 52455, 60427, 69372, 79392, 90627, 103143, 117065, 132561
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OFFSET
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0,3
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COMMENT
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These are the coefficients of the expansion in powers of z^4, the other coefficients being zero.
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REFERENCES
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J-M. Kantor, Ou en sont les mathematiques. La formule de Molien-Weyl, SMF, Vuibert, p. 79
T. Shioda, On the graded ring of invariants of binary octavics. Amer. J. Math. 89, 1022-1046, 1967.
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LINKS
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Index entries for Molien series
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FORMULA
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G.f.: (1+z^9+z^12+z^15+2*z^18+3*z^21+2*z^24+3*z^27+4*z^30+3*z^33+4*z^36+4*z^39 +3*z^42+4*z^45+3*z^48+2*z^51+3*z^54+2*z^57+z^60+z^63+z^75)/(1-z^3)/(1- z^6)/(1-z^9)/(1-z^12)/(1-z^15)/(1-z^18)/(1-z^27)
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MAPLE
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a(n)=coeff(coeff(coeff(simplify(convert(series((1+p*q+q^2/p-2*q-q^2)*((1-t)*(1-t\ *p)*(1-t*q)*(1-t*p^2)*(1-t*p*q)*(1-t*q^2)*(1-t*p^3)*(1-t*p^2*q)*(1-t*q^2*p)*(1-t\ *q^3)*(1-t*p^4)*(1-t*p^3*q)*(1-t*p^2*q^2)*(1-t*q^3*p)*(1-t*q^4))^(-1), t, n+1), polynom)), t^n), (p)^(n*d/3)), (q)^(n*d/3)); - Leonid Bedratyuk (bedratyuk(AT)ief.tup.km.ua), Jun 10 2008
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PROGRAM
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(PARI) a(n)=polcoeff((1+z^9+z^12+z^15+2*z^18+3*z^21+2*z^24+3*z^27+4*z^30+3*z^33 +4*z^36+4*z^39+3*z^42+4*z^45+3*z^48+2*z^51+3*z^54+2*z^57+z^60+z^63+z^75) /(1-z^3)/(1-z^6)/(1-z^9)/(1-z^12)/(1-z^15)/(1-z^18)/(1- z^27)+O(z^(n+1)), n)
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CROSSREFS
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Cf. A008615.
Sequence in context: A078513 A024622 A034337 this_sequence A003292 A007864 A118647
Adjacent sequences: A083021 A083022 A083023 this_sequence A083025 A083026 A083027
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 01 2003
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