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A041175
Denominators of continued fraction convergents to sqrt(97).
3
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
0,3
LINKS
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).
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
MATHEMATICA
Denominator[Convergents[Sqrt[97], 30]] (* Vincenzo Librandi, Dec 12 2013 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 14 2013
STATUS
approved