A041135 Denominators of continued fraction convergents to sqrt(76).
1, 1, 3, 4, 7, 39, 163, 854, 1017, 1871, 4759, 6630, 110839, 117469, 345777, 463246, 809023, 4508361, 18842467, 98720696, 117563163, 216283859, 550130881, 766414740, 12812766721, 13579181461, 39971129643, 53550311104, 93521440747, 521157514839, 2178151500103
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,115598,0,0,0,0,0,0,0,0,0,0,0,-1).
Programs
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Mathematica
Denominator/@Convergents[Sqrt[76], 50] (* Vladimir Joseph Stephan Orlovsky, Jul 05 2011 *)
Formula
a(n) = 115598*a(n-12)-a(n-24). G.f.: -(x^22 -x^21 +3*x^20 -4*x^19 +7*x^18 -39*x^17 +163*x^16 -854*x^15 +1017*x^14 -1871*x^13 +4759*x^12 -6630*x^11 -4759*x^10 -1871*x^9 -1017*x^8 -854*x^7 -163*x^6 -39*x^5 -7*x^4 -4*x^3 -3*x^2 -x -1)/((x^12-340*x^6+1)*(x^12+340*x^6+1)). [Colin Barker, Jul 19 2012]
Extensions
Formula corrected by Colin Barker, Jul 24 2012