|
|
A167617
|
|
G.f.: x^2*(3+3*x+x^2) / ( (2*x+1) * (1+x) * (1+x+x^2) * (x^2-x+1) ) .
|
|
2
|
|
|
0, 0, 3, -6, 10, -21, 42, -84, 171, -342, 682, -1365, 2730, -5460, 10923, -21846, 43690, -87381, 174762, -349524, 699051, -1398102, 2796202, -5592405, 11184810, -22369620, 44739243, -89478486, 178956970, -357913941, 715827882, -1431655764, 2863311531
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
The derived sequence a(n+1) + 2*a(n) reads 0,3,0,-2,-1,0 (and repeat with period 6).
|
|
LINKS
|
|
|
FORMULA
|
a(3*k+2) + a(3*k+3) + a(3*k+4) = (-1)^(k+1)*A024088(k+1).
a(n) = -3*a(n-1) -3*a(n-2) -3*a(n-3) -3*a(n-4) -3*a(n-5) -2*a(n-6).
|
|
MATHEMATICA
|
CoefficientList[Series[x^2(3+3x+x^2)/((2x+1)(1+x)(1+x+x^2)(x^2-x+1)), {x, 0, 40}], x] (* or *) LinearRecurrence[{-3, -3, -3, -3, -3, -2}, {0, 0, 3, -6, 10, -21}, 40] (* Harvey P. Dale, Sep 08 2011 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
sign,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|