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A204769 a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.

%I A204769 #35 Feb 28 2023 02:23:42
%S A204769 46,105,197,256,348,407,499,558,650,709,801,860,952,1011,1103,1162,
%T A204769 1254,1313,1405,1464,1556,1615,1707,1766,1858,1917,2009,2068,2160,
%U A204769 2219,2311,2370,2462,2521,2613,2672,2764,2823
%N A204769 a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.
%C A204769 Positive numbers k such that k^2 == 2 (mod 151), where the prime 151 == -1 (mod 8).
%C A204769 Equivalently, numbers k such that k == 46 or 105 (mod 151). - _Bruno Berselli_, Mar 08 2012
%H A204769 Vincenzo Librandi, <a href="/A204769/b204769.txt">Table of n, a(n) for n = 1..1000</a>
%H A204769 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A204769 G.f.: x*(46+59*x+46*x^2)/((1+x)*(x-1)^2).
%F A204769 a(n) = (-151-33*(-1)^n+302*n)/4.
%F A204769 a(n) = a(n-1) +a(n-2) -a(n-3).
%F A204769 Sum_{n>=1} (-1)^(n+1)/a(n) = tan(59*Pi/302)*Pi/151. - _Amiram Eldar_, Feb 28 2023
%t A204769 LinearRecurrence[{1,1,-1}, {46,105,197}, 40] (* or *) CoefficientList[Series[x*(46+59*x+46*x^2)/((1+x)*(x-1)^2),{x,0,33}],x] (* or *) a[1] = 46; a[n_] := a[n] = 151*(n-1) - a[n-1]; Table[a[n], {n, 1, 40}]
%o A204769 (Magma) [(-151-33*(-1)^n+302*n)/4: n in [1..60]];
%o A204769 (PARI) a(n)=(-151-33*(-1)^n+302*n)/4 \\ _Charles R Greathouse IV_, Oct 16 2015
%Y A204769 Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k-1: A047341, A155450, A164131, A164135, A167533, A167534, A177044, A177046, A204766.
%Y A204769 Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k+1: A155449, A158803, A159007, A159008, A176010, A206525.
%K A204769 nonn,easy
%O A204769 1,1
%A A204769 _Vincenzo Librandi_, Mar 08 2012