|
| |
|
|
A173127
|
|
a(n) = sinh((2n-1)*arcsinh(3)).
|
|
14
|
|
|
|
-3, 3, 117, 4443, 168717, 6406803, 243289797, 9238605483, 350823718557, 13322062699683, 505887558869397, 19210405174337403, 729489509065951917, 27701390939331835443, 1051923366185543794917, 39945386524111332371403
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Numbers n such that ((n^2 + 1)/10) is a square. - Vincenzo Librandi, Jan 02 2012
|
|
|
LINKS
|
Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (38,-1).
|
|
|
FORMULA
|
a(n) = (1/2)*((-3+sqrt(10))*(19+6*sqrt(10))^n + (-3-sqrt(10))*(19-6*sqrt(10))^n).
a(n) = -a(-n+1).
G.f.: -3*(1-39*x)/(1-38*x+x^2). - Bruno Berselli, Jan 03 2011
|
|
|
MATHEMATICA
|
Table[Round[N[Sinh[(2 n - 1) ArcSinh[3]], 100]], {n, 0, 20}]
Table[1/2 (-3 + Sqrt[10]) (19 + 6 Sqrt[10])^n + 1/2 (-3 - Sqrt[10]) (19 - 6 Sqrt[10]) ^n, {n, 0, 10}]
OR
Clear[a]; a[n_] := a[n] = 38 a[n - 1] - a[n - 2]; a[0] = -3; a[1] = 3; Table[a[n], {n, 0, 30}]
LinearRecurrence[{38, -1}, {-3, 3}, 30] (* Harvey P. Dale, Jan 14 2015 *)
|
|
|
PROG
|
(MAGMA) [-3], [n: n in [0..10^7]|IsSquare((n^2+1)/10)]; // Vincenzo Librandi, Jan 02 2012
|
|
|
CROSSREFS
|
Cf. A058331 A001079, A037270, A071253, A108741, A132592, A146311-A146313, A173115, A173116, A173121.
Sequence in context: A009491 A176614 A173797 * A230646 A006845 A071536
Adjacent sequences: A173124 A173125 A173126 * A173128 A173129 A173130
|
|
|
KEYWORD
|
sign,easy
|
|
|
AUTHOR
|
Artur Jasinski, Feb 10 2010
|
|
|
STATUS
|
approved
|
| |
|
|
