|
|
A255843
|
|
a(n) = 2*n^2 + 4.
|
|
16
|
|
|
4, 6, 12, 22, 36, 54, 76, 102, 132, 166, 204, 246, 292, 342, 396, 454, 516, 582, 652, 726, 804, 886, 972, 1062, 1156, 1254, 1356, 1462, 1572, 1686, 1804, 1926, 2052, 2182, 2316, 2454, 2596, 2742, 2892, 3046, 3204, 3366, 3532, 3702, 3876, 4054, 4236, 4422
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,1
|
|
COMMENTS
|
This is the case k=2 of the form (n + sqrt(k))^2 + (n - sqrt(k))^2.
Equivalently, numbers m such that 2*m - 8 is a square.
|
|
LINKS
|
|
|
FORMULA
|
G.f.: 2*(2 - 3*x + 3*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 + sqrt(2)*Pi*coth(sqrt(2)*Pi))/8.
Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(2)*Pi*cosech(sqrt(2)*Pi))/8. (End)
|
|
MATHEMATICA
|
Table[2 n^2 + 4, {n, 0, 50}]
|
|
PROG
|
(PARI) vector(50, n, n--; 2*n^2+4)
(Sage) [2*n^2+4 for n in (0..50)]
(Magma) [2*n^2+4: n in [0..50]];
|
|
CROSSREFS
|
Cf. unsigned A147973: numbers of the form 2*m^2-4.
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|