|
|
A241848
|
|
a(n) = n^2 + 18.
|
|
3
|
|
|
18, 19, 22, 27, 34, 43, 54, 67, 82, 99, 118, 139, 162, 187, 214, 243, 274, 307, 342, 379, 418, 459, 502, 547, 594, 643, 694, 747, 802, 859, 918, 979, 1042, 1107, 1174, 1243, 1314, 1387, 1462, 1539, 1618, 1699, 1782, 1867, 1954, 2043, 2134, 2227, 2322
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
LINKS
|
|
|
FORMULA
|
G.f.: (18 - 35*x + 19*x^2)/(1 - x)^3.
a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
Sum_{n>=0} 1/a(n) = (1 + sqrt(18)*Pi*coth(sqrt(18)*Pi))/36.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(18)*Pi*cosech(sqrt(18)*Pi))/36. (End)
|
|
MATHEMATICA
|
Table[n^2 + 18, {n, 0, 60}]
|
|
PROG
|
(Magma) [n^2+18: n in [0..60]];
|
|
CROSSREFS
|
Cf. similar sequences listed in A114962.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|