|
|
A178222
|
|
Partial sums of floor(3^n/4).
|
|
1
|
|
|
0, 2, 8, 28, 88, 270, 816, 2456, 7376, 22138, 66424, 199284, 597864, 1793606, 5380832, 16142512, 48427552, 145282674, 435848040, 1307544140, 3922632440, 11767897342, 35303692048, 105911076168, 317733228528
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
|
|
LINKS
|
|
|
FORMULA
|
a(n) = round((3*3^n - 4*n - 4)/8).
a(n) = floor((3*3^n - 4*n - 3)/8).
a(n) = ceiling((3*3^n - 4*n - 5)/8).
a(n) = round((3*3^n - 4*n - 3)/8).
a(n) = a(n-2) + 3^(n-1) - 1, n > 2.
a(n) = (3*3^n - 4*n - 4 + (-1)^n)/8.
G.f.: 2*x^2/((1+x)*(1-3*x)*(1-x)^2). (End)
|
|
EXAMPLE
|
a(3) = 0 + 2 + 6 = 8.
|
|
MAPLE
|
seq (round ((3*3^n-4*n-3)/8), n=1..25);
|
|
MATHEMATICA
|
CoefficientList[Series[2 x/((1 + x) (1 - 3 x) (1 - x)^2), {x, 0, 50}], x] (* Vincenzo Librandi, Mar 26 2014 *)
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|