A156866 - OEIS

%I #24 Sep 08 2022 08:45:41

%S 612180,1341180,2070180,2799180,3528180,4257180,4986180,5715180,

%T 6444180,7173180,7902180,8631180,9360180,10089180,10818180,11547180,

%U 12276180,13005180,13734180,14463180,15192180,15921180,16650180,17379180

%N a(n) = 729000*n - 116820.

%C The identity (32805000*n^2 - 10513800*n + 842401)^2 - (2025*n^2 - 3401*n + 1428)*(729000*n - 116820)^2 = 1 can be written as A157079(n)^2 - A156854(n)*a(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A156866/b156866.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*a(n-1) - a(n-2).

%F G.f.: 180*x*(3401+649*x)/(1-x)^2.

%F E.g.f.: 180*(649 - (649 - 4050*x)*exp(x)). - _G. C. Greubel_, Jan 28 2022

%t LinearRecurrence[{2,-1},{612180,1341180},40]

%o (Magma) I:=[612180, 1341180]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

%o (PARI) a(n)=729000*n-116820 \\ _Charles R Greathouse IV_, Dec 23 2011

%o (Sage) [180*(4050*n -649) for n in (1..40)] # _G. C. Greubel_, Jan 28 2022

%Y Cf. A156854, A156865, A157079.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 17 2009