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%I #19 Jan 04 2023 19:04:50
%S 25,26,77,1951,3979,5930,300479,306409,913297,23138834,47190965,
%T 70329799,3563680915,3634010714,10831702343,274426569289,559684840921,
%U 834111410210,42265255351421,43099366761631
%N Numerators of continued fraction convergents to sqrt(659).
%H Vincenzo Librandi, <a href="/A042266/b042266.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 11860, 0, 0, 0, 0, 0, -1).
%F G.f.: (25 + 26*x + 77*x^2 + 1951*x^3 + 3979*x^4 + 5930*x^5 + 3979*x^6 - 1951*x^7 + 77*x^8 - 26*x^9 + 25*x^10 - x^11)/(1 - 11860*x^6 + x^12). - _Vincenzo Librandi_, Nov 20 2013
%F a(n) = 11860*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 18 2013
%t Numerator[Convergents[Sqrt[659], 30]] (* or *) CoefficientList[Series[(25 + 26 x + 77 x^2 + 1951 x^3 + 3979 x^4 + 5930 x^5 + 3979 x^6 - 1951 x^7 + 77 x^8 - 26 x^9 + 25 x^10 - x^11)/(1 - 11860 x^6 + x^12), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 20 2013 *)
%t LinearRecurrence[{0,0,0,0,0,11860,0,0,0,0,0,-1},{25,26,77,1951,3979,5930,300479,306409,913297,23138834,47190965,70329799},30] (* _Harvey P. Dale_, Jan 04 2023 *)
%o (Magma) I:=[25,26,77,1951,3979,5930,300479,306409,913297,23138834, 47190965,70329799]; [n le 12 select I[n] else 11860*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013
%Y Cf. A042267.
%K nonn,cofr,frac,easy
%O 0,1
%A _N. J. A. Sloane_.