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%I #28 Feb 28 2023 02:23:09
%S 38,65,141,168,244,271,347,374,450,477,553,580,656,683,759,786,862,
%T 889,965,992,1068,1095,1171,1198,1274,1301,1377,1404,1480,1507,1583,
%U 1610,1686,1713,1789,1816,1892,1919,1995,2022,2098,2125,2201,2228,2304,2331,2407,2434,2510,2537
%N a(n) = 103*(n-1)-a(n-1) with n>1, a(1)=38.
%C Positive numbers k such that k^2 == 2 (mod 103).
%H Vincenzo Librandi, <a href="/A177044/b177044.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 (1,1,-1).
%F a(n) = (103+49*(-1)^(n-1)+206*(n-1))/4.
%F G.f.: x*(38+27*x+38*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Aug 24 2011
%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(27*Pi/206)*Pi/103. - _Amiram Eldar_, Feb 28 2023
%t CoefficientList[Series[(38 + 27 x + 38 x^2)/((1 + x) (x - 1)^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Sep 24 2014 *)
%t LinearRecurrence[{1,1,-1},{38,65,141},50] (* _Harvey P. Dale_, Nov 21 2021 *)
%o (Magma) [(103+49*(-1)^(n-1)+206*(n-1))/(4): n in [1..50]];
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Dec 09 2010
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