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%I M2162 #45 Sep 03 2022 22:23:24
%S 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) = (5n+1)^2 + 4n+1.
%C Also, numbers of the form (3k+1)^2 + (4k+1)^2. - _Bruno Berselli_, Dec 11 2011
%C The continued fraction expansion of sqrt(a(n)) is [5n+1; {2, 2, 10n+2}]. For n=0, this collapses to [1; {2}]. - _Magus K. Chu_, Aug 27 2022
%D W. Sierpiński, Elementary Theory of Numbers. Państ. Wydaw. Nauk., Warsaw, 1964, p. 323.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H Vincenzo Librandi, <a href="/A007533/b007533.txt">Table of n, a(n) for n = 0..1000</a>
%H W. Sierpiński, <a href="https://eudml.org/doc/219306">Elementary Theory of Numbers</a>, Warszawa 1964.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _Bruno Berselli_, Dec 11 2011: (Start)
%F a(n) = 25n^2 + 14n + 2.
%F G.f.: (2 + 35*x + 13*x^2)/(1-x)^3. (End)
%t Table[25n^2+14n+2,{n,0,40}] (* or *) LinearRecurrence[{3,-3,1},{2,41,130},40] (* _Harvey P. Dale_, Dec 18 2013 *)
%o (Magma) [(5*n+1)^2 + 4*n+1: n in [0..40]]; // _Vincenzo Librandi_, May 02 2011
%o (PARI) a(n)=25*n^2 + 14*n + 2 \\ _Charles R Greathouse IV_, May 02 2011
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, _Robert G. Wilson v_
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