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%I #21 Mar 11 2024 07:10:20
%S -3,3,117,4443,168717,6406803,243289797,9238605483,350823718557,
%T 13322062699683,505887558869397,19210405174337403,729489509065951917,
%U 27701390939331835443,1051923366185543794917,39945386524111332371403
%N a(n) = sinh((2n-1)*arcsinh(3)).
%C Numbers n such that ((n^2 + 1)/10) is a square. - _Vincenzo Librandi_, Jan 02 2012
%H Vincenzo Librandi, <a href="/A173127/b173127.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (38,-1).
%F a(n) = (1/2)*((-3+sqrt(10))*(19+6*sqrt(10))^n + (-3-sqrt(10))*(19-6*sqrt(10))^n).
%F a(n) = -a(-n+1).
%F G.f.: -3*(1-39*x)/(1-38*x+x^2). - _Bruno Berselli_, Jan 03 2011
%t LinearRecurrence[{38,-1},{-3,3},30] (* _Harvey P. Dale_, Jan 14 2015 *)
%o (Magma) [-3],[n: n in [0..10^7]|IsSquare((n^2+1)/10)]; // _Vincenzo Librandi_, Jan 02 2012
%Y Cf. A058331 A001079, A037270, A071253, A108741, A132592, A146311-A146313, A173115, A173116, A173121.
%K sign,easy
%O 0,1
%A _Artur Jasinski_, Feb 10 2010
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