cp's OEIS Frontend

A173127 a(n) = sinh((2n-1)*arcsinh(3)).

%I A173127 #33 Apr 24 2025 17:33:41
%S A173127 -3,3,117,4443,168717,6406803,243289797,9238605483,350823718557,
%T A173127 13322062699683,505887558869397,19210405174337403,729489509065951917,
%U A173127 27701390939331835443,1051923366185543794917,39945386524111332371403
%N A173127 a(n) = sinh((2n-1)*arcsinh(3)).
%C A173127 Numbers n such that ((n^2 + 1)/10) is a square. - _Vincenzo Librandi_, Jan 02 2012
%H A173127 Vincenzo Librandi, <a href="/A173127/b173127.txt">Table of n, a(n) for n = 0..200</a>
%H A173127 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (38,-1).
%F A173127 a(n) = (1/2)*((-3+sqrt(10))*(19+6*sqrt(10))^n + (-3-sqrt(10))*(19-6*sqrt(10))^n).
%F A173127 a(n) = -a(-n+1).
%F A173127 G.f.: -3*(1-39*x)/(1-38*x+x^2). - _Bruno Berselli_, Jan 03 2011
%F A173127 E.g.f.: exp(19*x)*(-3*cosh(6*sqrt(10)*x) + sqrt(10)*sinh(6*sqrt(10)*x)). - _Stefano Spezia_, Apr 24 2025
%t A173127 LinearRecurrence[{38,-1},{-3,3},30] (* _Harvey P. Dale_, Jan 14 2015 *)
%o A173127 (Magma) [-3] cat [n: n in [0..10^7]|IsSquare((n^2+1)/10)]; // _Vincenzo Librandi_, Jan 02 2012
%o A173127 (Python)
%o A173127 from itertools import islice
%o A173127 def A173127_gen(): # generator of terms
%o A173127     x, y = -30, 10
%o A173127     while True:
%o A173127         yield x//10
%o A173127         x, y = x*19+y*60, x*6+y*19
%o A173127 A173127_list = list(islice(A173127_gen(),20)) # _Chai Wah Wu_, Apr 24 2025
%Y A173127 Cf. A058331 A001079, A037270, A071253, A108741, A132592, A146311-A146313, A173115, A173116, A173121.
%K A173127 sign,easy
%O A173127 0,1
%A A173127 _Artur Jasinski_, Feb 10 2010