|
|
A155966
|
|
a(n) = 2*n^2 + 8.
|
|
4
|
|
|
8, 10, 16, 26, 40, 58, 80, 106, 136, 170, 208, 250, 296, 346, 400, 458, 520, 586, 656, 730, 808, 890, 976, 1066, 1160, 1258, 1360, 1466, 1576, 1690, 1808, 1930, 2056, 2186, 2320, 2458, 2600, 2746, 2896, 3050, 3208, 3370, 3536, 3706, 3880, 4058
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
The identity (n^3+4*n)^2 + (2*n^2+8)^2 = (n^2+4)^3 can be written as A155965(n)^2 + a(n)^2 = A087475(n)^3.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 2*(4 - 7*x + 5*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
Sum_{n>=0} 1/a(n) = 1/16 + coth(2*Pi)*Pi/8.
Sum_{n>=0} (-1)^n/a(n) = 1/16 + cosech(2*Pi)*Pi/8. (End)
|
|
MATHEMATICA
|
|
|
PROG
|
|
|
CROSSREFS
|
Cf. similar sequences listed in A255843.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
Offset changed from 1 to 0 and added a(0)=8 by Bruno Berselli, Mar 13 2015
|
|
STATUS
|
approved
|
|
|
|