|
|
A008456
|
|
12th powers: a(n) = n^12.
|
|
26
|
|
|
0, 1, 4096, 531441, 16777216, 244140625, 2176782336, 13841287201, 68719476736, 282429536481, 1000000000000, 3138428376721, 8916100448256, 23298085122481, 56693912375296, 129746337890625, 281474976710656, 582622237229761
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Numbers which are square, cubic and quartic. - Doug Bell, Jun 03 2017
|
|
LINKS
|
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
|
|
FORMULA
|
Sum_{n>=1} 1/a(n) = zeta(12) = 691*Pi^12/638512875 (A013670).
Sum_{n>=1} (-1)^(n+1)/a(n) = 2047*zeta(12)/2048 = 1414477*Pi^12/1307674368000. (End)
a(n) = 13*a(n-1)-78*a(n-2)+286*a(n-3)-715*a(n-4)+1287*a(n-5)-1716*a(n-6)+1716*a(n-7)-1287*a(n-8)+715*a(n-9)-286*a(n-10)+78*a(n-11)-13*a(n-12)+a(n-13). - Wesley Ivan Hurt, Dec 02 2021
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy,mult
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|