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A100025
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Molien series for complete weight enumerators of trace-additive Hermitian self-dual codes over the Galois ring GR(4,2) that contain the all-ones vector.
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0
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1, 1, 7, 21, 92, 291, 981, 2871, 8134, 21131, 52481, 122759, 275356, 590289, 1220811, 2436045, 4715827, 8866230, 16246890, 29054190, 50830264, 87104226, 146467614, 241934106, 393098860, 628867434, 991602894, 1542350194, 2368492984, 3593354974
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OFFSET
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0,3
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LINKS
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Table of n, a(n) for n=0..29.
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Index entries for Molien series
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FORMULA
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G.f.: u1/u2 where u1 := f(t) + t^41*f(1/t), u2 := (1-t)*(1-t^2)^6*(1-t^4)^7*(1-t^8)^2 and
f(t) := 1 + 14*t^3 + 43*t^4 + 115*t^5 + 334*t^6 + 808*t^7 + 1752*t^8 + 3557*t^9 + 6448*t^10 + 10800*t^11 + 17020*t^12 + 24972*t^13 + 34704*t^14 + 45824*t^15 + 57298*t^16 + 68464*t^17 + 78120*t^18 + 85092*t^19 + 88922*t^20.
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MAPLE
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f := 1 + 14*t^3 + 43*t^4 + 115*t^5 + 334*t^6 + 808*t^7 + 1752*t^8 + 3557*t^9 + 6448*t^10 + 10800*t^11 + 17020*t^12 + 24972*t^13 + 34704*t^14 + 45824*t^15 + 57298*t^16 + 68464*t^17 + 78120*t^18 + 85092*t^19 + 88922*t^20;
u1 := f + t^41*subs(t=1/t, f); u2 := (1-t)*(1-t^2)^6*(1-t^4)^7*(1-t^8)^2;
seq(coeff(series(u1/u2, t, n+1), t, n), n = 0..45); # Georg Fischer, Jan 25 2021
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CROSSREFS
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Sequence in context: A114902 A177369 A164544 * A121157 A347863 A253072
Adjacent sequences: A100022 A100023 A100024 * A100026 A100027 A100028
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KEYWORD
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nonn
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AUTHOR
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G. Nebe (nebe(AT)math.rwth-aachen.de), Nov 10, 2004
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STATUS
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approved
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