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A092070
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Molien series for genus 2 complete weight enumerators of self-dual codes over GF(3) containing the all-ones vector.
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0
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1, 2, 13, 87, 472, 2099, 7651, 23632, 64007, 155869, 347888, 722562, 1412787, 2623960, 4663042, 7975064, 13188959, 21174366, 33109962, 50565794, 75601497, 110881127, 159807508, 226678408, 316865230, 437017617, 595296931, 801638887, 1068049576, 1408938228
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OFFSET
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0,2
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COMMENTS
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The invariant ring for a 9-dimensional group Z_4 X 3^{1+4}_{+}.SP_4(3) of order 50388480.
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LINKS
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Index entries for linear recurrences with constant coefficients, signature (3,-2,1,-6,7,-3,4,-5,7,-5,-4,0,4,5,-7,5,-4,3,-7,6,-1,2,-3,1).
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MAPLE
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# (Maple code for Molien series:)
f := 1+8*t^2+60*t^3+292*t^4+1090*t^5+3127*t^6+7116*t^7 +13411*t^8 + 21536*t^9+29963*t^10+36631*t^11+39638*t^12 +37973*t^13+32135*t^14+ 23906*t^15+15462*t^16+8507*t^17 +3858*t^18+1369*t^19+342*t^20+52*t^21+3*t^22;
u1 := subs(t=t^12, f); u2 := (1-t^12)^2*(1-t^24)^2*(1-t^36)^3*(1-t^60)^2; MS := u1/u2;
seq(coeff(series(MS, t, 12*n+3), t, 12*n), n=0..30);
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MATHEMATICA
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CoefficientList[Series[(1+8*x^2+60*x^3+292*x^4+1090*x^5+3127*x^6+7116*x^7 +13411*x^8 + 21536*x^9+29963*x^10+36631*x^11+39638*x^12 +37973*x^13+32135*x^14+ 23906*x^15+15462*x^16+8507*x^17 +3858*x^18+1369*x^19+342*x^20+52*x^21+3*x^22) / (-(x+1)^2*(x^4+x^3+x^2+x+1)^2*(x^2+x+1)^3*(x-1)^9), {x, 0, 28}], x] (* Georg Fischer, Jan 25 2021 *)
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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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