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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

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OFFSET

0,1

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).

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).

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 *)

PROG

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

(SageMath)

def A122192_list(prec):

P.<x> = 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

CROSSREFS

Cf. A001380, A123013.