|
|
A173962
|
|
Averages of two consecutive odd cubes; a(n) = (n^3+(n+2)^3)/2.
|
|
3
|
|
|
14, 76, 234, 536, 1030, 1764, 2786, 4144, 5886, 8060, 10714, 13896, 17654, 22036, 27090, 32864, 39406, 46764, 54986, 64120, 74214, 85316, 97474, 110736, 125150, 140764, 157626, 175784, 195286, 216180, 238514, 262336, 287694, 314636, 343210
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
(1^3 + 3^3)/2 = 14,..
|
|
LINKS
|
|
|
FORMULA
|
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4). - Colin Barker, Jan 17 2015
G.f.: 2*x*(7*x^2+10*x+7) / (x-1)^4. - Colin Barker, Jan 17 2015
|
|
MATHEMATICA
|
f[n_]:=(n^3+(n+2)^3)/2; Table[f[n], {n, 1, 6!, 2}]
Mean/@Partition[Range[1, 81, 2]^3, 2, 1] (* Harvey P. Dale, Apr 20 2015 *)
|
|
PROG
|
(PARI) Vec(2*x*(7*x^2+10*x+7)/(x-1)^4 + O(x^100)) \\ Colin Barker, Jan 17 2015
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|