A041073 Denominators of continued fraction convergents to sqrt(43).
1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884, 46435951, 50133835, 96569786, 339843193, 436412979, 2521908088, 2958321067, 11396871289, 14355192356, 25752063645, 323379956096, 349132019741
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Les Tablettes du Chercheur, Problem 364, pp. 11, Mai 15 1891.
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,6964,0,0,0,0,0,0,0,0,0,-1).
Programs
-
Magma
I:=[1, 1, 2, 7, 9, 52, 61, 235, 296, 531, 6668, 7199, 13867, 48800, 62667, 362135, 424802, 1636541, 2061343, 3697884]; [n le 20 select I[n] else 6964*Self(n-10)-Self(n-20): n in [1..40]]; // Vincenzo Librandi, Dec 10 2013
-
Mathematica
Denominator[Convergents[Sqrt[43], 40]] (* Vincenzo Librandi, Dec 10 2013 *)
Formula
G.f.: -(x^18 -x^17 +2*x^16 -7*x^15 +9*x^14 -52*x^13 +61*x^12 -235*x^11 +296*x^10 -531*x^9 -296*x^8 -235*x^7 -61*x^6 -52*x^5 -9*x^4 -7*x^3 -2*x^2 -x -1) / (x^20 -6964*x^10 +1). - Colin Barker, Nov 12 2013
a(n) = 6964*a(n-10) - a(n-20). - Vincenzo Librandi, Dec 10 2013
Extensions
More terms from Colin Barker, Nov 12 2013