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%I #33 Jan 17 2021 02:52:25
%S 3,5,9,15,23,33,45,59,75,93,113,135,159,185,213,243,275,309,345,383,
%T 423,465,509,555,603,653,705,759,815,873,933,995,1059,1125,1193,1263,
%U 1335,1409,1485,1563,1643,1725,1809,1895,1983,2073,2165,2259
%N a(n) = n^2 + n + 3.
%H Colin Barker, <a href="/A027688/b027688.txt">Table of n, a(n) for n = 0..1000</a>
%H Patrick De Geest, <a href="http://www.worldofnumbers.com/quasimor.htm">Palindromic Quasi_Over_Squares of the form n^2+(n+X)</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F For n>0: a(n) = A176271(n+1,2). - _Reinhard Zumkeller_, Apr 13 2010
%F a(n) = 2*n + a(n-1) (with a(0)=3). - _Vincenzo Librandi_, Aug 05 2010
%F From _Colin Barker_, Dec 29 2014: (Start)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
%F G.f.: (3*x^2 - 4*x + 3)/(1 - x)^3. (End)
%F Sum_{n>=0} 1/a(n) = Pi*tanh(Pi*sqrt(11)/2)/sqrt(11). - _Amiram Eldar_, Jan 17 2021
%p with (combinat):seq(fibonacci(3, n)+n+2, n=0..47); # _Zerinvary Lajos_, Jun 07 2008
%t Table[n^2 + n + 3, {n, 0, 50}] (* _Bruno Berselli_, Sep 03 2018 *)
%o (PARI) Vec((3*x^2-4*x+3)/(1-x)^3 + O(x^100)) \\ _Colin Barker_, Dec 29 2014
%Y Cf. A002522.
%K nonn,easy
%O 0,1
%A _Patrick De Geest_
%E Definition and offset corrected by _Franklin T. Adams-Watters_, Jul 06 2009
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