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A083024 Molien series for action of SL(3,C) on ternary forms of degree 4. 0
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

These are the coefficients of the expansion in powers of z^4, the other coefficients being zero.

REFERENCES

J-M. Kantor, Où en sont les mathématiques. La formule de Molien-Weyl, SMF, Vuibert, p. 79

LINKS

Table of n, a(n) for n=0..45.

T. Shioda, On the graded ring of invariants of binary octavics, Amer. J. Math. 89, 1022-1046, 1967.

Index entries for Molien series

FORMULA

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).

MAPLE

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, Jun 10 2008

PROG

(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)

CROSSREFS

Cf. A008615.

Sequence in context: A170804 A024622 A034337 * A003292 A007864 A277271

Adjacent sequences:  A083021 A083022 A083023 * A083025 A083026 A083027

KEYWORD

nonn

AUTHOR

Benoit Cloitre, Jun 01 2003

STATUS

approved

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Last modified June 16 12:38 EDT 2019. Contains 324152 sequences. (Running on oeis4.)