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%I #25 Sep 08 2022 08:46:07
%S 19,20,23,28,35,44,55,68,83,100,119,140,163,188,215,244,275,308,343,
%T 380,419,460,503,548,595,644,695,748,803,860,919,980,1043,1108,1175,
%U 1244,1315,1388,1463,1540,1619,1700,1783,1868,1955,2044,2135,2228,2323
%N a(n) = n^2 + 19.
%H Vincenzo Librandi, <a href="/A241849/b241849.txt">Table of n, a(n) for n = 0..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.: (19 - 37*x + 20*x^2)/(1 - x)^3.
%F a(n) = a(-n) = 3*a(n-1) - 3*a(n-2) + a(n-3) = a(n-1) + 2*n - 1.
%F From _Amiram Eldar_, Nov 03 2020: (Start)
%F Sum_{n>=0} 1/a(n) = (1 + sqrt(19)*Pi*coth(sqrt(19)*Pi))/38.
%F Sum_{n>=0} (-1)^n/a(n) = (1 + sqrt(19)*Pi*cosech(sqrt(19)*Pi))/38. (End)
%p A241849:=n->n^2+19: seq(A241849(n), n=0..100); # _Wesley Ivan Hurt_, Jan 16 2017
%t Table[n^2 + 19, {n, 0, 60}]
%t LinearRecurrence[{3,-3,1},{19,20,23},50] (* _Harvey P. Dale_, Dec 05 2018 *)
%o (Magma) [n^2+19: n in [0..60]];
%o (PARI) a(n)=n^2+19 \\ _Charles R Greathouse IV_, Jun 17 2017
%Y Cf. similar sequences listed in A114962.
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, May 01 2014
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