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%I A041251 #20 Jul 09 2025 00:30:39
%S A041251 1,1,3,7,10,17,44,105,149,3383,3532,10447,24426,34873,59299,153471,
%T A041251 366241,519712,11799905,12319617,36439139,85197895,121637034,
%U A041251 206834929,535306892,1277448713,1812755605,41158072023,42970827628,127099727279,297170282186
%N A041251 Denominators of continued fraction convergents to sqrt(137).
%H A041251 Vincenzo Librandi, <a href="/A041251/b041251.txt">Table of n, a(n) for n = 0..200</a>
%H A041251 <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,3488,0,0,0,0,0,0,0,0,1).
%F A041251 G.f.: -(x^16 -x^15 +3*x^14 -7*x^13 +10*x^12 -17*x^11 +44*x^10 -105*x^9 +149*x^8 +105*x^7 +44*x^6 +17*x^5 +10*x^4 +7*x^3 +3*x^2 +x +1) / (x^18 +3488*x^9 -1). - _Colin Barker_, Nov 14 2013
%F A041251 a(n) = 3488*a(n-9) + a(n-18). - _Vincenzo Librandi_, Dec 13 2013
%t A041251 Denominator[Convergents[Sqrt[137], 30]]  (* _Vincenzo Librandi_, Dec 13 2013 *)
%t A041251 LinearRecurrence[{0,0,0,0,0,0,0,0,3488,0,0,0,0,0,0,0,0,1},{1,1,3,7,10,17,44,105,149,3383,3532,10447,24426,34873,59299,153471,366241,519712},40] (* _Harvey P. Dale_, Oct 29 2022 *)
%o A041251 (Magma) I:=[1,1,3,7,10,17,44,105,149,3383,3532,10447,24426,34873,59299, 153471,366241,519712]; [n le 18 select I[n] else 3488*Self(n-9)+Self(n-18): n in [1..40]]; // _Vincenzo Librandi_, Dec 13 2013
%Y A041251 Cf. A041250, A010196.
%K A041251 nonn,frac,easy
%O A041251 0,3
%A A041251 _N. J. A. Sloane_
%E A041251 More terms from _Colin Barker_, Nov 14 2013

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