A041124 Numerators of continued fraction convergents to sqrt(71).
8, 17, 42, 59, 455, 514, 1483, 3480, 57163, 117806, 292775, 410581, 3166842, 3577423, 10321688, 24220799, 397854472, 819929743, 2037713958, 2857643701, 22041219865, 24898863566, 71838946997, 168576757560, 2769067067957, 5706710893474, 14182488854905
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1).
Programs
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Mathematica
Numerator[Convergents[Sqrt[71], 30]] (* Vincenzo Librandi, Oct 29 2013 *) LinearRecurrence[{0,0,0,0,0,0,0,6960,0,0,0,0,0,0,0,-1},{8,17,42,59,455,514,1483,3480,57163,117806,292775,410581,3166842,3577423,10321688,24220799},40] (* Harvey P. Dale, Aug 14 2023 *)
Formula
G.f.: -(x^15 -8*x^14 +17*x^13 -42*x^12 +59*x^11 -455*x^10 +514*x^9 -1483*x^8 -3480*x^7 -1483*x^6 -514*x^5 -455*x^4 -59*x^3 -42*x^2 -17*x -8) / (x^16 -6960*x^8 +1). - Colin Barker, Nov 05 2013
Extensions
More terms from Colin Barker, Nov 05 2013