A041106 Numerators of continued fraction convergents to sqrt(61).
7, 8, 39, 125, 164, 453, 1070, 1523, 5639, 24079, 29718, 440131, 469849, 2319527, 7428430, 9747957, 26924344, 63596645, 90520989, 335159612, 1431159437, 1766319049, 26159626123, 27925945172, 137863406811, 441516165605, 579379572416, 1600275310437
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,59436,0,0,0,0,0,0,0,0,0,0,1).
Programs
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Mathematica
Numerator[Convergents[Sqrt[61], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
Formula
G.f.: -(x^21 -7*x^20 +8*x^19 -39*x^18 +125*x^17 -164*x^16 +453*x^15 -1070*x^14 +1523*x^13 -5639*x^12 +24079*x^11 +29718*x^10 +24079*x^9 +5639*x^8 +1523*x^7 +1070*x^6 +453*x^5 +164*x^4 +125*x^3 +39*x^2 +8*x +7) / (x^22 +59436*x^11 -1). - Colin Barker, Nov 12 2013
Extensions
More terms from Colin Barker, Nov 12 2013