A156867 - OEIS

%I #22 Sep 08 2022 08:45:41

%S 728820,1457820,2186820,2915820,3644820,4373820,5102820,5831820,

%T 6560820,7289820,8018820,8747820,9476820,10205820,10934820,11663820,

%U 12392820,13121820,13850820,14579820,15308820,16037820,16766820,17495820

%N a(n) = 729000*n - 180.

%C The identity (32805000*n^2 - 16200*n + 1)^2 - (2025*n^2 - n)* (729000*n - 180)^2 = 1 can be written as A157080(n)^2 - A156855(n)*a(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A156867/b156867.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.: x*(728820+180*x)/(1-x)^2.

%F E.g.f.: 180*(1 - (1 - 4050*x)*exp(x)). - _G. C. Greubel_, Jan 28 2022

%t LinearRecurrence[{2,-1},{728820,1457820},40]

%o (Magma) I:=[728820, 1457820]; [n le 2 select I[n] else 2*Self(n-1)-Self(n-2): n in [1..40]];

%o (PARI) a(n)=729000*n-180 \\ _Charles R Greathouse IV_, Dec 23 2011

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

%Y Cf. A156855, A156868, A157080.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 17 2009