A122192 Sum of the n-th powers of the roots of the (reduced) weight enumerator of the extended Golay code (1 + 759*x^2 + 2576*x^3 + 759*x^4 + x^6).

6, 0, -1518, -7728, 1149126, 9775920, -851127150, -10374206304, 619950551814, 10059106207584, -443172509029998, -9223980220220304, 309985135145332422, 8134978519171135632, -211181377213616588526, -6965969413257227260608, 139095682365347347024902

Offset: 0

Author

N. J. A. Sloane, Nov 12 2006

Keywords

• sign
• easy

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500
• Index entries for linear recurrences with constant coefficients, signature (0,-759,-2576,-759,0,-1).

Crossrefs

Cf. A001380, A123013.

Programs

Maple

Newt:=proc(f) local t1,t2,t3,t4; t1:=f; t2:=diff(f,x); t3:=expand(x^degree(t1,x)*subs(x=1/x,t1)); t4:=expand(x^degree(t2,x)*subs(x=1/x,t2)); factor(t4/t3); end;
g:=1+759*x^2+2576*x^3+759*x^4+x^6; Newt(g); series(%,x,60);

Mathematica

LinearRecurrence[{0,-759,-2576,-759,0,-1}, {6,0,-1518,-7728,1149126,9775920}, 30] (* G. C. Greubel, Jul 11 2021 *)

PARI

polsym(x^6 + 759*x^4 + 2576*x^3 + 759*x^2 + 1, 30) \\ Charles R Greathouse IV, Jul 20 2016

Sage

def A122192_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( 6*(1+506*x^2+1288*x^3+253*x^4)/(1+759*x^2+2576*x^3+759*x^4 +x^6) ).list()
A122192_list(30) # G. C. Greubel, Jul 11 2021

Formula

G.f.: 6*(1 + 506*x^2 + 1288*x^3 + 253*x^4)/(1 + 759*x^2 + 2576*x^3 + 759*x^4 + x^6).