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A041381
Denominators of continued fraction convergents to sqrt(205).
2
1, 3, 19, 22, 107, 129, 881, 2772, 78497, 238263, 1508075, 1746338, 8493427, 10239765, 69932017, 220035816, 6230934865, 18912840411, 119707977331, 138620817742, 674191248299, 812812066041, 5551063644545, 17466002999676, 494599147635473, 1501263445906095
OFFSET
0,2
LINKS
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,79378,0,0,0,0,0,0,0,-1).
FORMULA
G.f.: -(x^14 -3*x^13 +19*x^12 -22*x^11 +107*x^10 -129*x^9 +881*x^8 -2772*x^7 -881*x^6 -129*x^5 -107*x^4 -22*x^3 -19*x^2 -3*x -1) / (x^16 -79378*x^8 +1). - Colin Barker, Nov 16 2013
a(n) = 79378*a(n-8) - a(n-16) for n>15. - Vincenzo Librandi, Dec 16 2013
MATHEMATICA
Denominator[Convergents[Sqrt[205], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 79378, 0, 0, 0, 0, 0, 0, 0, -1}, {1, 3, 19, 22, 107, 129, 881, 2772, 78497, 238263, 1508075, 1746338, 8493427, 10239765, 69932017, 220035816}, 30] (* Harvey P. Dale, Apr 17 2022 *)
PROG
(Magma) I:=[1, 3, 19, 22, 107, 129, 881, 2772, 78497, 238263, 1508075, 1746338, 8493427, 10239765, 69932017, 220035816]; [n le 16 select I[n] else 79378*Self(n-8)-Self(n-16): n in [1..40]]; // Vincenzo Librandi, Dec 16 2013
CROSSREFS
Sequence in context: A043073 A359314 A022128 * A042231 A191074 A019408
KEYWORD
nonn,frac,easy
AUTHOR
EXTENSIONS
More terms from Colin Barker, Nov 16 2013
STATUS
approved