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

1, 2, 12, 84, 660, 5548, 48836, 444412, 4147220, 39471436, 381671204, 3738957148, 37028943860, 370123733932, 3729092573060, 37831802166076, 386135110256852, 3962278590508812, 40852572573083364, 423006921400424988, 4396894566694687924

Offset

0,2

Comments

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

Links

Fung Lam, Table of n, a(n) for n = 0..1000

Formula

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

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

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

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

Prog

(Python)
# a235351. The list a has been calculated (len(a)>=3).
m = len(a)+1
d = 0
for i in range (1, m):
....for j in range (1, m):
........if (i+j)%m ==0 and (i+j) <= m:
............d = d + a[i-1]*a[j-1]
g = 0
for i in range (1, m):
....for j in range (1, m):
........for k in range (1, m):
............if (i+j+k)%m ==0 and (i+j+k) <= m:
................g = g + a[i-1]*a[j-1]*a[k-1]
y = 2*g + 3*d - a[m-2]
# a235351.

Crossrefs

Cf. A107841, A235349.

Sequence in context: A006657 A105927 A316702 * A362245 A362237 A052887

Adjacent sequences: A235348 A235349 A235350 * A235352 A235353 A235354

Keyword

nonn,easy

Author

Fung Lam, Jan 16 2014

Status

approved