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 A235351 Series reversion of x*(1-3*x-2*x^2)/(1-x). 1

%I #15 Mar 24 2023 15:00:22

%S 1,2,12,84,660,5548,48836,444412,4147220,39471436,381671204,

%T 3738957148,37028943860,370123733932,3729092573060,37831802166076,

%U 386135110256852,3962278590508812,40852572573083364,423006921400424988,4396894566694687924

%N Series reversion of x*(1-3*x-2*x^2)/(1-x).

%C Derived turbulence series: combined series reversion of A107841 and A235349.

%H Fung Lam, <a href="/A235351/b235351.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: (exp(4*Pi*i/3)*u + exp(2*Pi*i/3)*v - 1/2)/x, where i=sqrt(-1),

%F u = 1/6*(-54-81*x+3*sqrt(-51+522*x+549*x^2-24*x^3))^(1/3), and

%F v = 1/6*(-54-81*x-3*sqrt(-51+522*x+549*x^2-24*x^3))^(1/3).

%F First few terms can be obtained by Maclaurin's expansion of G.f.D-finite with recurrence 17*n*(n+1)*(11*n-17)*a(n) -n*(1914*n^2-3915*n+1513)*a(n-1) +(-2013*n^3+7137*n^2-7924*n+2640)*a(n-2) +4*(2*n-5)*(11*n-6)*(n-2)*a(n-3)=0. - _R. J. Mathar_, Jun 14 2016

%o (Python)

%o # a235351. The list a has been calculated (len(a)>=3).

%o m = len(a)+1

%o d = 0

%o for i in range (1,m):

%o ....for j in range (1,m):

%o ........if (i+j)%m ==0 and (i+j) <= m:

%o ............d = d + a[i-1]*a[j-1]

%o g = 0

%o for i in range (1,m):

%o ....for j in range (1,m):

%o ........for k in range (1,m):

%o ............if (i+j+k)%m ==0 and (i+j+k) <= m:

%o ................g = g + a[i-1]*a[j-1]*a[k-1]

%o y = 2*g + 3*d - a[m-2]

%o # a235351.

%Y Cf. A107841, A235349.

%K nonn,easy

%O 0,2

%A _Fung Lam_, Jan 16 2014

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Last modified November 29 00:31 EST 2023. Contains 367422 sequences. (Running on oeis4.)