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A241406 Numbers n such that n^2 == -1 (mod 61).

%I A241406 #16 Sep 21 2024 15:12:55
%S A241406 11,50,72,111,133,172,194,233,255,294,316,355,377,416,438,477,499,538,
%T A241406 560,599,621,660,682,721,743,782,804,843,865,904,926,965,987,1026,
%U A241406 1048,1087,1109,1148,1170,1209,1231,1270,1292,1331,1353,1392,1414,1453,1475,1514
%N A241406 Numbers n such that n^2 == -1 (mod 61).
%C A241406 Numbers n such that n == 11 or 50 (mod 61).
%H A241406 Vincenzo Librandi, <a href="/A241406/b241406.txt">Table of n, a(n) for n = 1..1000</a>
%H A241406 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A241406 G.f.: x*(11 + 39*x + 11*x^2)/((1 + x)*(1 - x)^2).
%F A241406 a(n) = a(n-1) + a(n-2) - a(n-3) for n>2.
%F A241406 a(n) = a(n-2) + 61 for all n>2.
%F A241406 a(n) = -11*(-1)^n + 61*floor(n/2).
%t A241406 Select[Range[1500], PowerMod[#, 2, 61] == 60 &] (* or *) CoefficientList[Series[(11 + 39 x + 11 x^2)/((1 + x) (1 - x)^2), {x, 0, 100}], x]
%o A241406 (Magma) I:=[11,50,72]; [n le 3 select I[n] else Self(n-1)+Self(n-2)-Self(n-3): n in [1..50]];
%o A241406 (Magma) [-11*(-1)^n+61*Floor(n/2): n in [1..50]];
%Y A241406 Cf. similar sequences listed in A155107.
%K A241406 nonn,easy
%O A241406 1,1
%A A241406 _Vincenzo Librandi_, Apr 25 2014