|
|
A274272
|
|
Number of partitions of 5^n into at most four parts.
|
|
2
|
|
|
1, 6, 185, 15246, 1736385, 212946246, 26516391385, 3312004971246, 413937039016385, 51740540399346246, 6467527813385891385, 808439983261977471246, 101054973072475964016385, 12631871013177766274346246, 1578983861125177809948391385
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Coefficient of x^(5^n) in 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
Conjectures (Start)
a(n) = (57+8*(-1)^n+63*5^n+3*5^(1+2*n)+125^n)/144.
a(n) = 155*a(n-1)-3874*a(n-2)+15470*a(n-3)+3875*a(n-4)-15625*a(n-5) for n>4.
G.f.: (1-149*x+3129*x^2-5655*x^3-6750*x^4) / ((1-x)*(1+x)*(1-5*x)*(1-25*x)*(1-125*x)).
(End)
|
|
PROG
|
(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)).
b(n) = round(real(68+36*(-1)^n+18*((-I)^n+I^n)+(16*exp(-2/3*I*n*Pi)*(1+I*sqrt(3)+2*exp((4*I*n*Pi)/3)))/(1+(-1)^(1/3))+59*(1+n)+9*(-1)^n*(1+n)+18*(1+n)*(2+n)+2*(1+n)*(2+n)*(3+n))/288)
vector(20, n, n--; b(5^n))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|