A041175 Denominators of continued fraction convergents to sqrt(97).
1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352, 120205801, 126583153, 753121566, 879704719, 1632826285, 2512531004, 4145357289, 6657888293, 10803245582, 60674116203, 71477361785
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,11208,0,0,0,0,0,0,0,0,0,0,1).
Programs
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Magma
I:=[1, 1, 6, 7, 13, 20, 33, 53, 86, 483, 569, 10725, 11294, 67195, 78489, 145684, 224173, 369857, 594030, 963887, 5413465, 6377352]; [n le 22 select I[n] else 11208*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 12 2013
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Mathematica
Denominator[Convergents[Sqrt[97], 30]] (* Vincenzo Librandi, Dec 12 2013 *)
Formula
G.f.: -(x^20 -x^19 +6*x^18 -7*x^17 +13*x^16 -20*x^15 +33*x^14 -53*x^13 +86*x^12 -483*x^11 +569*x^10 +483*x^9 +86*x^8 +53*x^7 +33*x^6 +20*x^5 +13*x^4 +7*x^3 +6*x^2 +x +1) / (x^22 +11208*x^11 -1). - Colin Barker, Nov 14 2013
a(n) = 11208*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 12 2013
Extensions
More terms from Colin Barker, Nov 14 2013