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%I #32 Nov 25 2016 02:33:13
%S 5,7,11,17,25,35,47,61,77,95,115,137,161,187,215,245,277,311,347,385,
%T 425,467,511,557,605,655,707,761,817,875,935,997,1061,1127,1195,1265,
%U 1337,1411,1487,1565,1645,1727,1811,1897,1985,2075,2167,2261
%N a(n) = n^2 + n + 5.
%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 a(n) = A176271(n + 1, 3) for n > 1. - _Reinhard Zumkeller_, Apr 13 2010
%F a(n) = 2*n + a(n-1) for n>0, a(0)=5. - _Vincenzo Librandi_, Aug 05 2010
%F From _Ilya Gutkovskiy_, Nov 25 2016: (Start)
%F G.f.: (5 - 8*x + 5*x^2)/(1 - x)^3.
%F Sum_{n>=0} 1/a(n) = Pi*tanh(sqrt(19)*Pi/2)/sqrt(19) = 0.720729156259... (End)
%p with (combinat):seq(fibonacci(3, n)+n+4, n=0..47); # _Zerinvary Lajos_, Jun 07 2008
%t Table[n^2 + n + 5, {n, 0, 100}] (* _T. D. Noe_, Oct 29 2009 *)
%o (PARI) a(n)=n^2+n+5 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A002061, A002522.
%K nonn,easy
%O 0,1
%A _Patrick De Geest_
%E Corrected by _T. D. Noe_, Nov 09 2006
%E Definition and offset fixed by _Franklin T. Adams-Watters_, Jul 06 2009
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