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A092547 Molien series for complete weight enumerators of Type II self-dual codes over Z/8Z containing the all-ones vector. 4
1, 13, 673, 8485, 54806, 239653, 810554, 2286970, 5645962, 12569202, 25774647, 49439178, 89715139, 155363247, 258516275, 415556399, 648154544, 984466839, 1460477524, 2121535332, 3024090172, 4237589492, 5846620281, 7953274324, 10679706157, 14170967905 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
G. Nebe, E. M. Rains and N. J. A. Sloane, Self-Dual Codes and Invariant Theory, Springer, Berlin, 2006.
Index entries for linear recurrences with constant coefficients, signature (3,-1,-2,-4,4,9,-5,-6,-5,9,4,-4,-2,-1,3,-1).
FORMULA
G.f.: u1/u2 where u1 := subs(x=x^16, f); u2 := (1-x^16 )^3*(1-x^32 )^2*(1-x^48 )^3; and f := 1 + 10*x + 635*x^2 + 6481*x^3 + 30054*x^4 + 85114 *x^5 + 166002 *x^6 + 235709 *x^7 + 254210 *x^8 + 205865 *x^9 + 123812 *x^10 + 53334 *x^11 + 15059 *x^12 + 2247 *x^13 + 115 *x^14.
G.f.: (1 +10*x +635*x^2 +6481*x^3 +30054*x^4 +85114*x^5 +166002*x^6 +235709*x^7 +254210*x^8 +205865*x^9 +123812*x^10 +53334*x^11 +15059*x^12 +2247*x^13 +115*x^14)/( (1-x)^3*(1-x^2)^2*(1-x^3)^3 ). - G. C. Greubel, Feb 02 2020
MAPLE
f(x):= (1 +10*x +635*x^2 +6481*x^3 +30054*x^4 +85114*x^5 +166002*x^6 +235709*x^7 +254210*x^8 +205865*x^9 +123812*x^10 +53334*x^11 +15059*x^12 +2247*x^13 +115*x^14)/( (1-x)^3*(1-x^2)^2*(1-x^3)^3 );
seq(coeff(series( f(x), x, n+1), x, n), n = 0..30); # G. C. Greubel, Feb 02 2020
MATHEMATICA
CoefficientList[Series[(1 +10*x +635*x^2 +6481*x^3 +30054*x^4 +85114*x^5 +166002*x^6 +235709*x^7 +254210*x^8 +205865*x^9 +123812*x^10 +53334*x^11 +15059*x^12 +2247*x^13 +115*x^14)/( (1-x)^3*(1-x^2)^2*(1-x^3)^3 ), {x, 0, 30}], x] (* G. C. Greubel, Feb 02 2020 *)
LinearRecurrence[{3, -1, -2, -4, 4, 9, -5, -6, -5, 9, 4, -4, -2, -1, 3, -1}, {1, 13, 673, 8485, 54806, 239653, 810554, 2286970, 5645962, 12569202, 25774647, 49439178, 89715139, 155363247, 258516275, 415556399}, 30] (* Harvey P. Dale, Oct 31 2021 *)
CROSSREFS
Sequence in context: A217380 A068232 A363864 * A298951 A157027 A042307
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 09 2004
STATUS
approved

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Last modified March 29 06:44 EDT 2024. Contains 371265 sequences. (Running on oeis4.)