OFFSET
0,2
COMMENTS
This sequence was chosen to illustrate a way to match generating functions and closed-form solutions.
The general term associated with the generating function
1/((1-s*x)^4*(1-r*x)) with r>s>=1 is a(n) = [ r^(n+4) - s^(n+1)*(s^3 + s^2*(r-s)*binomial(n+4,1) + s*(r-s)^2*binomial(n+4,2)+(r-s)^3*binomial(n+4,3))]/(r-s)^4.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-30,40,-25,6).
FORMULA
a(n) = (6^(n+4) - (1 + 5*C(n+4,1) + 25*C(n+4,2) + 125*C(n+4,3)))/625 = (6^(n+5) - (125*n^3 + 1200*n^2 + 3805*n + 4026))/3750.
EXAMPLE
a(3) = (6^8 - (125*3^3 + 1200*3^2 + 3805*3 + 4026))/3750 = 440.
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Yahia Kahloune, Sep 27 2013
STATUS
approved