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A221875 Numbers m such that 10*m^2 - 6 is a square.

%I A221875 #36 Mar 16 2024 11:20:44
%S A221875 1,7,31,265,1177,10063,44695,382129,1697233,14510839,64450159,
%T A221875 551029753,2447408809,20924619775,92937084583,794584521697,
%U A221875 3529161805345,30173287204711,134015211518527,1145790329257321,5089048875898681,43509859224573487
%N A221875 Numbers m such that 10*m^2 - 6 is a square.
%C A221875 See the first two comments on A221874.
%C A221875 For the corresponding numbers whose square is 10*m^2 - 6, see A281647. - _Jon E. Schoenfield_, Aug 05 2023
%H A221875 Vincenzo Librandi, <a href="/A221875/b221875.txt">Table of n, a(n) for n = 1..1000</a>
%H A221875 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,38,0,-1).
%F A221875 G.f.: x*(1-x)*(1+8*x+x^2)/((1-6*x-x^2)*(1+6*x-x^2)).
%F A221875 a(n) = ((5-t*(-1)^n)*(3+t)^(2*floor(n/2)) + (5+t*(-1)^n)*(3-t)^(2*floor(n/2)))/10, where t=sqrt(10).
%F A221875 a(n)*a(n-3) - a(n-1)*a(n-2) = 36 + 12(-1)^n.
%t A221875 LinearRecurrence[{0, 38, 0, -1}, {1, 7, 31, 265}, 22]
%o A221875 (Magma)
%o A221875 m:=22; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!((1-x)*(1+8*x+x^2)/((1-6*x-x^2)*(1+6*x-x^2))));
%o A221875 (Maxima)
%o A221875 makelist(expand(((5-sqrt(10)*(-1)^n)*(3+sqrt(10))^(2*floor(n/2))+(5+sqrt(10)*(-1)^n)*(3-sqrt(10))^(2*floor(n/2)))/10), n, 1, 22);
%o A221875 (Magma) I:=[1, 7, 31, 265]; [n le 4 select I[n] else 38*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Mar 25 2013
%Y A221875 Cf. A221874, A281647.
%K A221875 nonn,easy
%O A221875 1,2
%A A221875 _Bruno Berselli_, Jan 28 2013