OFFSET
0,2
COMMENTS
This sequence was chosen to illustrate a method of solution.
LINKS
Index entries for linear recurrences with constant coefficients, signature (19, -123, 305, -200).
FORMULA
a(n) = (2*8^(n+4) - (84*n+287)*5^(n+2) - 9)/1008.
In general, for the expansion of 1/((1-t)*((1-s)^2)*(1-r)) with r > s > t, we have the formula: a(n) = (K*r^(n+3) + L*s^(n+3) + M*s^(n+2) + N*t^(n+3))/D, where K, L, M, N, D have the following values:
K = (s-t)^2;
L = (r-t)*(r-2*s+t);
M = -(r-s)*(r-t)*(s-t)*(n+3);
N = -(r-s)^2;
D = (r-t)*((s-t)^2)*((r-s)^2).
Directly using formula we get: a(n) = (16*8^(n+3) - 7*5^(n+3) -84*(n+3)*5^n+2) - 9)/1008. After transformation we obtain previous formula.
CROSSREFS
KEYWORD
nonn
AUTHOR
Yahia Kahloune, Sep 18 2013
STATUS
approved