OFFSET
0,3
LINKS
Fung Lam, Table of n, a(n) for n = 0..950
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).
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)
a = [0, 1]
for n in range(20):
m = len(a)
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]*a[j]
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]*a[j]*a[k]
y = 2*g + 3*d - a[m-1]
a.append(y)
print(a)
(PARI)
my(x='x+O('x^25)); concat([0], Vec(serreverse(x*(1-3*x-2*x^2)/(1-x)))) \\ Joerg Arndt, Sep 01 2024
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Fung Lam, Jan 16 2014
EXTENSIONS
a(0) = 0 prepended by Andrey Zabolotskiy, Aug 31 2024
STATUS
approved