A158797 - OEIS

%I #20 Jan 03 2024 08:48:52

%S 1,6,42,258,1770,11058,74778,472866,3164874,20188050,134123514,

%T 860893314,5689339818,36681499122,241497732570,1562031700962,

%U 10255950073482,66489091308114,435703293953466,2829310581045570

%N a(n) = a(n-1) + 36*a(n-2), a(0)=1, a(1)=6.

%H G. C. Greubel, <a href="/A158797/b158797.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 (1,36).

%F G.f.: (1+5*x)/(1-x-36*x^2).

%F a(n) = (6*i)^n*( ChebyshevU(n, -i/12) - (5*i/6)*ChebyshevU(n-1, -i/12) ). - _G. C. Greubel_, Dec 22 2021

%t LinearRecurrence[{1,36},{1,6},30] (* _Harvey P. Dale_, Apr 30 2013 *)

%o (PARI) Vec((1+5*x)/(1-x-36*x^2)+O(x^99)) \\ _Charles R Greathouse IV_, Jan 17 2012

%o (Sage) [(6*i)^n*( chebyshev_U(n, -i/12) - (5*i/6)*chebyshev_U(n-1, -i/12) ) for n in (0..40)] # _G. C. Greubel_, Dec 22 2021

%o (Magma) I:=[1,6]; [n le 2 select I[n] else Self(n-1) + 36*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Dec 22 2021

%Y Cf. A000045, A026597, A122994, A122995, A158608.

%K nonn,easy,less

%O 0,2

%A _Philippe Deléham_, Mar 27 2009