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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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0
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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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COMMENTS
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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, Où en sont les mathématiques. La formule de Molien-Weyl, SMF, Vuibert, p. 79
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (1,1,0,0,-1,0,-2,0,2,0,0,1,0,-1,0,1,0,-1,0,0,-2,0,2,0,1,0,0,-1,-1,1).
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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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seq(coeff(series( (1 + x^3 + x^4 + x^5 + 2*x^6 + 3*x^7 + 2*x^8 + 3*x^9 + 4*x^10 + 3*x^11 + 4*x^12 + 4*x^13 + 3*x^14 + 4*x^15 + 3*x^16 + 2*x^17 + 3*x^18 + 2*x^19 + x^20 + x^21 + x^25)/(1 - x^1 - x^2 + x^5 + 2*x^7 - 2*x^9 - x^12 + x^14 - x^16 + x^18 + 2*x^21 - 2*x^23 - x^25 + x^28 + x^29 - x^30), x, n+1), x, n), n = 0..45); # Georg Fischer, Jan 24 2021
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PROG
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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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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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