A083024 Molien series for action of SL(3,C) on ternary forms of degree 4.

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

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

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).

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

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

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