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%I #28 Feb 29 2024 15:55:15
%S 18,36,58,84,114,148,186,228,274,324,378,436,498,564,634,708,786,868,
%T 954,1044,1138,1236,1338,1444,1554,1668,1786,1908,2034,2164,2298,2436,
%U 2578,2724,2874,3028,3186,3348,3514,3684,3858,4036,4218,4404,4594,4788
%N a(n) = 2*n^2 + 12*n + 4.
%C Sixth diagonal of A144562.
%C 2*a(n) + 28 is a square.
%H Vincenzo Librandi, <a href="/A154575/b154575.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F From _R. J. Mathar_, Jan 05 2011: (Start)
%F a(n) = 2*A028881(n+3).
%F G.f.: -2*x*(2*x-3)*(x-3) / (x-1)^3. (End)
%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 26 2012
%F From _Amiram Eldar_, Feb 25 2023: (Start)
%F Sum_{n>=1} 1/a(n) = 1/28 - cot(sqrt(7)*Pi)*Pi/(4*sqrt(7)).
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 31/84 - cosec(sqrt(7)*Pi)*Pi/(4*sqrt(7)). (End)
%t LinearRecurrence[{3, -3, 1}, {18, 36, 58}, 50] (* _Vincenzo Librandi_, Feb 26 2012 *)
%t Table[2n^2+12n+4,{n,50}] (* _Harvey P. Dale_, Sep 18 2019 *)
%o (Magma) I:=[18, 36, 58]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // _Vincenzo Librandi_, Feb 26 2012
%o (PARI) for(n=1, 50, print1(2*n^2+12*n+4", ")); \\ _Vincenzo Librandi_, Feb 26 2012
%Y Cf. A028881, A144562, A153238, A067076.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 12 2009
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