A157078 - OEIS

%I #26 Sep 08 2022 08:45:41

%S 842401,44161201,153090001,327628801,567777601,873536401,1244905201,

%T 1681884001,2184472801,2752671601,3386480401,4085899201,4850928001,

%U 5681566801,6577815601,7539674401,8567143201,9660222001,10818910801,12043209601

%N a(n) = 32805000*n^2 - 55096200*n + 23133601.

%C The identity(32805000*n^2 - 55096200*n + 23133601)^2 - (2025*n^2 - 649*n + 52)*(729000*n - 612180)^2 = 1 can be written as a(n)^2 - A156853(n)*A156865(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A157078/b157078.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

%F G.f.: x*(842401 + 41633998*x + 23133601*x^2)/(1-x)^3.

%F E.g.f.: -23133601 + (23133601 - 22291200*x + 32805000*x^2)*exp(x). - _G. C. Greubel_, Jan 27 2022

%t LinearRecurrence[{3,-3,1},{842401,44161201,153090001},40]

%o (Magma) I:=[842401, 44161201, 153090001]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..30]];

%o (PARI) a(n)=32805000*n^2-55096200*n+23133601 \\ _Charles R Greathouse IV_, Dec 23 2011

%o (Sage) [16200*n*(2025*n - 3401) + 23133601 for n in (1..25)] # _G. C. Greubel_, Jan 27 2022

%Y Cf. A156853, A156865, A157079, A157080, A157081.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Feb 22 2009