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A097870 Molien series for group of order 4608 acting on joint weight enumerators of a pair of binary doubly-even self-dual codes. 2
1, 2, 4, 10, 17, 27, 45, 66, 92, 130, 173, 223, 289, 362, 444, 546, 657, 779, 925, 1082, 1252, 1450, 1661, 1887, 2145, 2418, 2708, 3034, 3377, 3739, 4141, 4562, 5004, 5490, 5997, 6527, 7105, 7706, 8332, 9010, 9713, 10443, 11229, 12042, 12884, 13786, 14717, 15679 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
COMMENTS
This is the Molien series for the group of order 128 discussed in A097869 extended by the extra generator diag{1,1,i,i}. This group was not considered in the reference cited.
The first g.f. inserts zeros between each pair of terms; the second g.f. does not. - Colin Barker, Feb 12 2015
LINKS
F. J. MacWilliams, C. L. Mallows and N. J. A. Sloane, Generalizations of Gleason's theorem on weight enumerators of self-dual codes, IEEE Trans. Inform. Theory, 18 (1972), 794-805.
FORMULA
G.f.: (1 + x^2 + 2*x^3 + x^4 + x^5 + x^6 + x^7)/(1 - 2*x + x^2 - 2*x^3 +
4*x^4 - 2*x^5 + x^6 - 2*x^7 + x^8).
G.f.: (1+x)*(1-x+x^2)*(1+x^2+x^3+x^4) / ((1-x)^4*(1+x+x^2)^2). - Colin Barker, Feb 12 2015
MAPLE
m:=50; S:=series((1+x^3)*(1+x^2+x^3+x^4)/((1-x)*(1-x^3))^2, x, m+1): seq(coeff(S, x, j), j=0..m); # G. C. Greubel, Feb 05 2020
MATHEMATICA
CoefficientList[Series[(1+x^3)*(1+x^2+x^3+x^4)/((1-x)*(1-x^3))^2, {x, 0, 50}], x] (* G. C. Greubel, Feb 05 2020 *)
LinearRecurrence[{2, -1, 2, -4, 2, -1, 2, -1}, {1, 2, 4, 10, 17, 27, 45, 66}, 50] (* Harvey P. Dale, Jun 11 2022 *)
PROG
(PARI) Vec((x+1)*(x^2-x+1)*(x^4+x^3+x^2+1)/((x-1)^4*(x^2+x+1)^2) + O(x^100)) \\ Colin Barker, Feb 12 2015
(Magma) R<x>:=PowerSeriesRing(Integers(), 50); Coefficients(R!( (1+x^3)*(1+x^2+x^3+x^4)/((1-x)*(1-x^3))^2 )); // G. C. Greubel, Feb 05 2020
(Sage)
def A097870_list(prec):
P.<x> = PowerSeriesRing(ZZ, prec)
return P( (1+x^3)*(1+x^2+x^3+x^4)/((1-x)*(1-x^3))^2 ).list()
A097870_list(50) # G. C. Greubel, Feb 05 2020
CROSSREFS
Cf. A097869.
Sequence in context: A264585 A077635 A125754 * A244474 A301739 A152231
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Sep 02 2004
STATUS
approved

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Last modified July 21 20:59 EDT 2024. Contains 374475 sequences. (Running on oeis4.)