A041107 Denominators of continued fraction convergents to sqrt(61).

1, 1, 5, 16, 21, 58, 137, 195, 722, 3083, 3805, 56353, 60158, 296985, 951113, 1248098, 3447309, 8142716, 11590025, 42912791, 183241189, 226153980, 3349396909, 3575550889, 17651600465, 56530352284, 74181952749, 204894257782, 483970468313, 688864726095

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,59436,0,0,0,0,0,0,0,0,0,0,1).

Formula

G.f.: -(x^20 -x^19 +5*x^18 -16*x^17 +21*x^16 -58*x^15 +137*x^14 -195*x^13 +722*x^12 -3083*x^11 +3805*x^10 +3083*x^9 +722*x^8 +195*x^7 +137*x^6 +58*x^5 +21*x^4 +16*x^3 +5*x^2 +x +1) / (x^22 +59436*x^11 -1). - Colin Barker, Nov 12 2013

a(n) = 59436*a(n-11) + a(n-22). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator[Convergents[Sqrt[61], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

Prog

(Magma) I:=[1, 1, 5, 16, 21, 58, 137, 195, 722, 3083, 3805, 56353, 60158, 296985, 951113, 1248098, 3447309, 8142716, 11590025, 42912791, 183241189, 226153980]; [n le 22 select I[n] else 59436*Self(n-11)+Self(n-22): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041106, A010145, A020818, A010514.

Sequence in context: A022140 A041855 A030691 * A042603 A031120 A395566

Adjacent sequences: A041104 A041105 A041106 * A041108 A041109 A041110

Keyword

nonn,cofr,easy,frac

Author

N. J. A. Sloane

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved