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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
OFFSET
0,1
COMMENTS
Numbers n such that ((n^2 + 1)/10) is a square. - Vincenzo Librandi, Jan 02 2012
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
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
KEYWORD
sign,easy
AUTHOR
Artur Jasinski, Feb 10 2010
STATUS
approved