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%I #46 Feb 01 2023 04:49:58
%S 13,2,41,130,269,458,697,986,1325,1714,2153,2642,3181,3770,4409,5098,
%T 5837,6626,7465,8354,9293,10282,11321,12410,13549,14738,15977,17266,
%U 18605,19994,21433,22922,24461,26050,27689,29378
%N a(n) = 25*n^2 - 36*n + 13.
%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 A154358(n)^2 - a(n)*A154360(n)^2 = 1. See also the third comment in A154357.
%C Numbers of the form (3n-2)^2 + (4n-3)^2. - _Bruno Berselli_, Dec 12 2011
%H Vincenzo Librandi, <a href="/A154355/b154355.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 a(n) = A007533(n-1), n>0. - _R. J. Mathar_, Jan 14 2009
%F G.f.: (13 - 37*x + 74*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). - _Vincenzo Librandi_, Feb 21 2012
%F E.g.f.: (13 - 11*x + 25*x^2)*exp(x). - _G. C. Greubel_, Sep 14 2016
%t Table[25n^2-36n+13,{n,0,40}] (* _Harvey P. Dale_, Apr 02 2011 *)
%t LinearRecurrence[{3, -3, 1}, {13, 2, 41}, 50] (* _Vincenzo Librandi_, Feb 21 2012 *)
%o (PARI) for(n=0, 40, print1(25*n^2 - 36*n + 13", ")); \\ _Vincenzo Librandi_, Feb 21 2012
%o (Magma) [25*n^2-36*n+13: n in [0..40]]; // _Bruno Berselli_, Sep 15 2016
%Y Cf. A154354, A154358-A154361, A202141.
%Y Essentially a duplicate of A007533.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Jan 07 2009
%E Offset corrected from _R. J. Mathar_, Jan 05 2011
%E First comment rewritten by _Bruno Berselli_, Dec 12 2011