A190986 - OEIS

%I #28 Dec 23 2023 09:45:15

%S 0,1,10,96,920,8816,84480,809536,7757440,74336256,712332800,

%T 6825982976,65410498560,626801053696,6006368542720,57556481212416,

%U 551539337953280,5285167454683136,50645517195018240,485314502131449856,4650562952534425600,44564371516818456576

%N a(n) = 10*a(n-1) - 4*a(n-2), with a(0)=0, a(1)=1.

%H G. C. Greubel, <a href="/A190986/b190986.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,-4).

%H <a href="/index/Ch#Cheby">Index entries for sequences related to Chebyshev polynomials.</a>

%F G.f.: x/(1 - 10*x + 4*x^2). - _Philippe Deléham_, Oct 12 2011

%F E.g.f.: (1/sqrt(21))*exp(5*x)*sinh(sqrt(21)*x). - _G. C. Greubel_, Sep 03 2022

%F a(n) = 2^(n-1)*S(n-1, 5), with the Chebyshev S-polynomial (see A049310) S(n-1, 5) = A004254(n). See the Magma program by _G. C. Greubel_. - _Wolfdieter Lang_, Nov 15 2023

%t LinearRecurrence[{10,-4}, {0,1}, 50]

%o (Magma) [2^(n-1)*Evaluate(ChebyshevU(n-1), 5/2): n in [0..30]]; // _G. C. Greubel_, Sep 03 2022

%o (SageMath)

%o A190986 = BinaryRecurrenceSequence(10, -4, 0, 1)

%o [A190986(n) for n in (0..30)] # _G. C. Greubel_, Sep 03 2022

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

%Y Cf. A004254, A049310.

%K nonn,easy

%O 0,3

%A _Vladimir Joseph Stephan Orlovsky_, May 24 2011