A041469 Denominators of continued fraction convergents to sqrt(250).
1, 1, 5, 16, 53, 228, 281, 8658, 8939, 44414, 142181, 470957, 2026009, 2496966, 76934989, 79431955, 394662809, 1263420382, 4184923955, 18003116202, 22188040157, 683644320912, 705832361069, 3506973765188, 11226753656633, 37187234735087, 159975692596981
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,8886,0,0,0,0,0,0,1).
Programs
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Magma
I:=[1,1,5,16,53,228,281,8658,8939,44414,142181, 470957,2026009,2496966]; [n le 14 select I[n] else 8886*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 18 2013
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Mathematica
Denominator[Convergents[Sqrt[250], 30]] (* Vincenzo Librandi, Dec 18 2013 *)
Formula
G.f.: -(x^12 -x^11 +5*x^10 -16*x^9 +53*x^8 -228*x^7 +281*x^6 +228*x^5 +53*x^4 +16*x^3 +5*x^2 +x +1) / (x^14 +8886*x^7 -1). - Colin Barker, Nov 18 2013
a(n) = 8886*a(n-7) + a(n-14) for n>13. - Vincenzo Librandi, Dec 18 2013
Extensions
More terms from Colin Barker, Nov 18 2013