login
A028344
Molien series for complete weight enumerator of self-dual code over GF(5).
1
1, 1, 1, 3, 4, 9, 19, 27, 41, 62, 91, 128, 175, 231, 298, 392, 498, 617, 768, 933, 1134, 1372, 1627, 1922, 2260, 2642, 3070, 3546, 4071, 4647, 5307, 6021, 6792, 7654, 8576, 9595, 10714, 11898, 13187, 14584
OFFSET
0,4
REFERENCES
Gagola, Stephen M., Jr. Weight enumerators of normalized codes. SIAM J. Algebraic Discrete Methods 2 (1981), no. 4, 347-380. MR0634360 (83e:94046). See Appendix, unnormalized codes, case q=5. N. J. A. Sloane, Apr 09 2014
LINKS
E. M. Rains and N. J. A. Sloane, Self-dual codes, pp. 177-294 of Handbook of Coding Theory, Elsevier, 1998 (Abstract, pdf, ps).
Index entries for linear recurrences with constant coefficients, signature (0, 1, 2, 0, 0, -1, -2, -3, 0, 3, 2, 1, 0, 0, -2, -1, 0, 1).
FORMULA
G.f.: (x^13 + 3*x^12 + 5*x^11 + 6*x^10 + 5*x^9 + 10*x^8 + 13*x^7 + 10*x^6 + 4*x^5 + x^4 + x + 1)/(-x^18 + x^16 + 2*x^15 - x^12 - 2*x^11 - 3*x^10 + 3*x^8 + 2*x^7 + x^6 - 2*x^3 - x^2 + 1) = (x^13 + 3*x^12 + 5*x^11 + 6*x^10 + 5*x^9 + 10*x^8 + 13*x^7 + 10*x^6 + 4*x^5 + x^4 + x + 1)/((1-x)^5*(1+x)*(1+x+x^2)^2*(1+x+x^2+x^3+x^4)^2). - Charles R Greathouse IV, Dec 08 2016
MAPLE
# Another program, from N. J. A. Sloane, Apr 09 2014
a:=[1, 1, 0, 0, 1, 4, 10, 13, 10, 5, 6, 5, 3, 1];
t:=n->1-x^n;
P:=add(a[i]*x^(i-1), i=1..nops(a))/(t(2)*t(3)^2*t(5)^2);
f:=tt->seriestolist(series(tt, x, 80));
MATHEMATICA
Take[CoefficientList[Series[(t^26 + 3*t^24 + 5*t^22 + 6*t^20 + 5*t^18 + 10*t^16 + 13*t^14 + 10*t^12 + 4*t^10 + t^8 + t^2 + 1)/( (1 - t^4)*(1 - t^6)^2*(1 - t^10)^2 ), {t, 0, 40}], t], {1, -1, 2}] (* G. C. Greubel, Nov 24 2016 *)
LinearRecurrence[{0, 1, 2, 0, 0, -1, -2, -3, 0, 3, 2, 1, 0, 0, -2, -1, 0, 1}, {1, 1, 1, 3, 4, 9, 19, 27, 41, 62, 91, 128, 175, 231, 298, 392, 498, 617}, 50] (* Robert G. Wilson v, Nov 25 2016 *)
CROSSREFS
Sequence in context: A374965 A178784 A192288 * A219680 A078010 A291532
KEYWORD
nonn,easy
STATUS
approved