A041101 Denominators of continued fraction convergents to sqrt(58).

1, 1, 2, 3, 5, 8, 13, 190, 203, 393, 596, 989, 1585, 2574, 37621, 40195, 77816, 118011, 195827, 313838, 509665, 7449148, 7958813, 15407961, 23366774, 38774735, 62141509, 100916244, 1474968925, 1575885169, 3050854094, 4626739263, 7677593357, 12304332620

Offset

0,3

Links

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

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,198,0,0,0,0,0,0,1).

Formula

G.f.: -(x^12 -x^11 +2*x^10 -3*x^9 +5*x^8 -8*x^7 +13*x^6 +8*x^5 +5*x^4 +3*x^3 +2*x^2 +x +1) / (x^14 +198*x^7 -1). - Colin Barker, Nov 12 2013

a(n) = 198*a(n-7) + a(n-14). - Vincenzo Librandi, Dec 11 2013

Mathematica

Denominator[Convergents[Sqrt[58], 30]] (* Vincenzo Librandi, Dec 11 2013 *)

Prog

(Magma) I:=[1, 1, 2, 3, 5, 8, 13, 190, 203, 393, 596, 989, 1585, 2574]; [n le 14 select I[n] else 198*Self(n-7)+Self(n-14): n in [1..40]]; // Vincenzo Librandi, Dec 11 2013

Crossrefs

Cf. A041100, A010143, A020815, A010511.

Sequence in context: A329192 A294939 A096095 * A041809 A117566 A123000

Adjacent sequences: A041098 A041099 A041100 * A041102 A041103 A041104

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 12 2013

Status

approved