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a(n) = 1250*n^2 - 1800*n + 649.
5

%I #27 Sep 08 2022 08:45:40

%S 649,99,2049,6499,13449,22899,34849,49299,66249,85699,107649,132099,

%T 159049,188499,220449,254899,291849,331299,373249,417699,464649,

%U 514099,566049,620499,677449,736899,798849,863299,930249

%N a(n) = 1250*n^2 - 1800*n + 649.

%C The identity (1250*n^2 - 1800*n + 649)^2 - (25*n^2 - 36*n + 13)*(250*n - 180)^2 = 1 can be written as a(n)^2 - A154355(n)*A154360(n)^2 = 1. See also the third comment in A154357.

%H Vincenzo Librandi, <a href="/A154358/b154358.txt">Table of n, a(n) for n = 0..10000</a>

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

%F G.f.: (649 - 1848*x + 3699*x^2)/(1-x)^3. - _R. J. Mathar_, Jan 05 2011

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

%F E.g.f.: (649 - 550*x + 1250*x^2)*exp(x). - _G. C. Greubel_, Sep 14 2016

%t LinearRecurrence[{3, -3, 1}, {649, 99, 2049}, 50] (* _Vincenzo Librandi_, Feb 21 2012 *)

%o (PARI) for(n=0, 40, print1(1250*n^2 - 1800*n + 649", ")); \\ _Vincenzo Librandi_, Feb 21 2012

%o (Magma) [1250*n^2-1800*n+649: n in [0..40]]; // _Bruno Berselli_, Sep 15 2016

%Y Cf. A154359, A154360, A154361, A154355, A154357.

%K nonn,easy

%O 0,1

%A _Vincenzo Librandi_, Jan 08 2009

%E Offset and one entry corrected by _R. J. Mathar_, Jan 05 2011

%E Librandi's comment rewritten by _Bruno Berselli_, Dec 13 2011