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A041104 Numerators of continued fraction convergents to sqrt(60).

%I A041104 #31 Aug 03 2015 11:30:33
%S A041104 7,8,23,31,457,488,1433,1921,28327,30248,88823,119071,1755817,1874888,
%T A041104 5505593,7380481,108832327,116212808,341257943,457470751,6745848457,
%U A041104 7203319208,21152486873,28355806081,418133772007,446489578088,1311112928183,1757602506271
%N A041104 Numerators of continued fraction convergents to sqrt(60).
%C A041104 Interspersion of 4 linear recurrences with constant coefficients. - _Gerry Martens_, Jun 10 2015
%H A041104 Vincenzo Librandi, <a href="/A041104/b041104.txt">Table of n, a(n) for n = 0..200</a>
%H A041104 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,62,0,0,0,-1).
%F A041104 G.f.: -(x^7-7*x^6+8*x^5-23*x^4-31*x^3-23*x^2-8*x-7) / ((x^4-8*x^2+1)*(x^4+8*x^2+1)). - _Colin Barker_, Nov 05 2013
%p A041104 numtheory:-cfrac(sqrt(60),50,'con'):
%p A041104 map(numer,con[1..-2]); # _Robert Israel_, Jun 09 2015
%t A041104 Numerator/@Convergents[Sqrt[60],30]  (* _Harvey P. Dale_, Apr 26 2011 *)
%t A041104 n0 := LinearRecurrence[{62, -1}, {7, 457}, 10]
%t A041104 n1 := LinearRecurrence[{62, -1}, {8, 488}, 10]
%t A041104 n2 := LinearRecurrence[{62, -1}, {23, 1433}, 10]
%t A041104 n3 := LinearRecurrence[{62, -1}, {31, 1921}, 10]
%t A041104 Flatten[MapIndexed[{n0[[#]],n1[[#]],n2[[#]],n3[[#]]} &, Range[10]]] (* _Gerry Martens_, Jun 09 2015 *)
%t A041104 LinearRecurrence[{0, 0, 0, 62, 0, 0, 0, -1},{7, 8, 23, 31, 457, 488, 1433, 1921},28] (* _Ray Chandler_, Aug 03 2015 *)
%Y A041104 Cf. A010513, A041105.
%K A041104 nonn,cofr,frac,easy
%O A041104 0,1
%A A041104 _N. J. A. Sloane_
%E A041104 More terms from _Colin Barker_, Nov 05 2013