|
%I #21 Feb 25 2023 06:33:30
%S 21,41,65,93,125,161,201,245,293,345,401,461,525,593,665,741,821,905,
%T 993,1085,1181,1281,1385,1493,1605,1721,1841,1965,2093,2225,2361,2501,
%U 2645,2793,2945,3101,3261,3425,3593,3765,3941,4121,4305,4493,4685,4881
%N a(n) = 2*n^2 + 14*n + 5.
%C Seventh diagonal in A144562.
%C 2*a(n) + 39 is a square.
%H Vincenzo Librandi, <a href="/A154576/b154576.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F G.f.: x*(3-x)*(7-5*x)/(1-x)^3. - _Bruno Berselli_, Dec 07 2011
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 22 2012
%F Sum_{n>=1} 1/a(n) = 124/1995 + tan(sqrt(39)*Pi/2)*Pi/(2*sqrt(39)). - _Amiram Eldar_, Feb 25 2023
%t LinearRecurrence[{3, -3, 1}, {21, 41, 65}, 50] (* _Vincenzo Librandi_, Feb 22 2012 *)
%o (Magma) I:=[21, 41, 65]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 22 2012
%o (PARI) for(n=1, 40, print1(2*n^2 + 14*n + 5", ")); \\ _Vincenzo Librandi_, Feb 22 2012
%Y Cf. A144562, A154577.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 12 2009
|
