A190987 - OEIS

%I #42 Dec 23 2023 09:45:12

%S 0,1,10,95,900,8525,80750,764875,7245000,68625625,650031250,

%T 6157184375,58321687500,552430953125,5232701093750,49564856171875,

%U 469485056250000,4447026281640625,42122837535156250,398993243943359375,3779318251757812500,35798216297861328125

%N a(n) = 10*a(n-1) - 5*a(n-2), with a(0)=0, a(1)=1.

%H G. C. Greubel, <a href="/A190987/b190987.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-5).

%F G.f.: x/(1 - 10*x + 5*x^2). - _Philippe Deléham_, Oct 12 2011

%F E.g.f.: (1/(2*sqrt(5)))*exp(5*x)*sinh(2*sqrt(5)*x). - _G. C. Greubel_, Sep 07 2022

%t LinearRecurrence[{10,-5}, {0,1}, 50]

%o (Magma) [Round(5^((n-1)/2)*Evaluate(ChebyshevU(n), Sqrt(5))): n in [0..30]]; // _G. C. Greubel_, Sep 07 2022

%o (SageMath)

%o A190987 = BinaryRecurrenceSequence(10, -5, 0, 1)

%o [A190987(n) for n in (0..30)] # _G. C. Greubel_, Sep 07 2022

%Y Cf. A190958 (index to generalized Fibonacci sequences).

%Y Cf. A019934 (sqrt(5-2*sqrt(5))), A019952 (sqrt(5+2*sqrt(5))).

%K nonn,easy

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, May 24 2011